It was a fairly logical combination of his parent's quirks: a movement-based quirk and a pyrokinetic (and therefore heat-based) quirk combined to make a quirk where heat could be moved around. Izuku's first intentional use was to keep his hands warm on a particularly cold day.
Bakugou was unimpressed. It was a quirk, sure, but keeping popsicles from melting and keeping dinner hot while finishing up a show weren't exactly comparable to explosions. Deku could make an explosion heatless, but it didn't save him from getting knocked flat on his ass.
But a quirk was a quirk, and Izuku was willing to put in the work. Advanced science classes simply showed him how his quirk could be applied in action, but it wasn't enough. He needed to know heat like he knew himself, he needed to understand it the same way All Might understood his muscles.
If that meant getting dense thermodynamics textbooks and using his allowance to get tutoring from college students- because his mother understood the book about as well as he did- then that was what he had to do.
There was complex stuff, of course, calculus that made his head swim and numerical magic he was just beginning to understand… but there were simpler things. Quirks had done a number on conventional physics, but in situations where they weren't involved the normal rules still applied.
(If a tree fell in a forest and no one used their quirk on it, it would hit the ground.)
Izuku's quirk did not break the first law. Some people broke the conservation of energy, but he did not. All he had was the total energy in a system… which was a whole awful lot, even discounting inaccessible gravitational and kinetic energy. They weren't at absolute zero, so he was sitting pretty.
The third law was a bit more cerebral, essentially saying that entropy approaches zero as the temperature of a system does. Good to know, but Izuku understood that he could make things colder by taking away heat ages before that.
Number two? That was the fun one. Put simply, heat isn't supposed to move from cold places to hot ones without work which generates more heat. On the grand scale, refrigerators are really just heaters. They make part of a system cool, but the heat they generate in the process counteracts that and then some. You can't get rid of heat without making more heat. A cruel law, previously ironclad…
But Izuku could break it in a second. He broke it every time he kept his drinks cold. Conservation of energy was nothing to a quirk.
(Well, there were scientists who speculated that quirks that seemed to break the laws of physics called upon some previously undiscovered wellspring of energy. Others called this cope.)
His studies also gave him a potential name. Maybe it was a little silly, but he liked the sound of Enthalpy, the Heat Hero. Better than the Thermodynamics Hero, at least.
(When Bakugou was caught up in the tendrils of the slime villain, it was the Heat Hero who sprung forward. He couldn't do anything to his muscles except keep them at their ideal temperature, but he ran anyway.
A wave of frost shot up the villain's side, making the villain sluggish. Not enough to stop him, although Izuku didn't care. His body moved on its own.)
The zero pointer loomed over the training ground, seeming as unassailable as a mountain. It was supposed to be invincible, as close as the UA staff could get to a natural disaster.
But Izuku had been using his power on electronics since he was ten. He knew how fiddly the insides of an electronic device were, and how much depended on delicate parts.
Heavy motor parts shrunk and grew brittle with the chill as a wave of heat shot up the arms, melting wiring into slag. Izuku couldn't be quite certain where the controls were, but the giant head seemed as good of a place to start as anywhere.
The temperature around the head plummeted, camera lenses cracking as heat plunged inside. For a moment, the robot continued moving, but it was nothing more than momentum. All of the delicate controls that kept the robot moving were ruined.
The monster panted, massive chest heaving as its eyes fixed on Izuku. For a moment, he froze, caught up in the terror of that horrible form and that bulging muscle, the exposed brain seemingly filled with nothing but thoughts of violence.
Izuku thought back to his classes and his books, thought about everything he knew about heat and cold and their interactions with the body.
The Nomu felt something almost like a body-wide chill, barring the exceptional heat that started in the hand and raced up the arm. Fire in the muscles of the chest, sliding through the muscles before tearing down the other arm. A moment of reprieve, of deathly, unstoppable cold as the heat traveled through the air before the fire began anew in the legs.
It attempted to step forward, to hunt down the source of the burning pain, but the arms could not move, the legs collapsed under the Nomu's tremendous mass.
Midoriya didn't know what exactly they would be facing for the sports festival, but he prepared. He had his own equipment, although he didn't have to go down to the Support students to get it. Really, all he needed to find was a water fountain. They couldn't have hero students being dehydrated on their big day, could they?
There was so much to water that went overlooked, despite the way it ruled their modern lives. The Industrial Revolution sprung from water, and some modern turbine engines still used it in their mechanisms.
While he had never spent much time with steam tables, he knew how water and steam behaved. When water became steam, the specific volume increased a thousandfold. What was specific volume? It was how much space a kilo of something took up.
Put simply? A kilo of steam filled more than a thousand times the amount of space that a kilo of water did. Very useful. Run a steam engine with it, whatever, but keep it carefully contained. Hot steam, after all, would scald.
Vaguely, he wondered if this would be setting a bad example for the kids watching this on television. Well, watching him get blown to high heaven would probably be worse…
Izuku angled his water bottle so the mouth was pointed towards the finish line, and he positioned himself in front of it. He would not do this if he wasn't supremely confident in his abilities, and even then, he was worried.
"WHAT'S THIS, FOLKS? MIDORIYA HAS STOPPED!"
Present Mic was making some sort of joke about him being thirsty or something, but Izuku didn't notice. Inhale, and feel the heat around him. It was all hot, even his water, when compared to absolute zero. There was so much heat just lying around…
Focus. Gather heat. From the ground, from the air, gather it thick around the bottle, don't let any of it seep out. Make a ball of incredible, unfathomable heat, shimmering like a mirage at the bottle's mouth. Throw it in.
It was, admittedly, a very special bottle, made of the strongest stuff UA could reasonably get him. It still might have exploded, he wasn't sure, but he was already too far away to care, shot away by a blast of steam.
If not for his quirk, he would have cooked, but he kept the cloud of heat from touching him or the other students, turning the heat into a mighty updraft to cushion his landing.
Still hurt, even with the updraft and a roll, but he managed to completely leap the minefield. He got up and kept running.
"You know, one of the hero names I didn't use was Maxwell," Midoriya spoke to Todoroki, but microphones picked up the sound so the whole arena could hear it.
Todoroki looked unimpressed. "Maxwell?" He asked, his breath a misty cloud in front of him.
"Yeah. It's the name of a scientist. He did a lot of interesting stuff, but he had this idea. He had a thought experiment about breaking the second law of thermodynamics. If a creature was smart enough and quick enough, it could sort hot and cold particles from each other. The skill and reaction speed needed would be insane… it was impossible, like every other potential violation of the law."
"Impossible," Midoriya repeated, the emotion in his voice building. "People spent their entire lives searching for something I can do as easily as breathing. I don't want to sound egotistical… but we're miracles, Todoroki."
Todoroki looked a little confused, but let Midoriya talk.
"The more I study, the more I realize how lucky I am. I'm lucky enough to have a quirk, and lucky enough that's it strong. I'm lucky to have the work of so many brilliant people who gave me a foundation." He stood on the shoulders of giants, even without a quirk that accumulated power through the generations.
Science built up power like that too.
"And that's what makes me so angry. That you can stand there with an incredible power and not use half of it. You disagree with how your father uses it? Use it better."
Technology and powers were not evil. It was how they were used.
Todoroki had heard enough. He sent a wave of ice Midoriya's way, too fast and too big for him to dodge, even with his athleticism.
The problem was that Midoriya didn't need to dodge. He stayed perfectly still as a person-shaped hole melted in the ice, not flinching even as he was essentially surrounded by an iceberg.
Sunlight reflected off of it brilliantly, shimmering in little streams and rivulets slipping down the sides. Those trickles became a flood as the entire iceberg melted in moments, revealing a miraculously dry Midoriya.
(Drying his clothes was child's play.)
"How about I make it fair? Go all out?" He grinned. Todoroki braced himself.
"Absolute Zero." Midoriya breathed, an explosion of sheer cold covering the arena in frost and freezing people's drinks all the way up in the stands.
Well, explosion was probably the wrong word, considering the brilliant pinprick that hung in the air like a star, seething with the heat of an entire stadium.
Midoriya doesn't actually set the arena to absolute zero at the end, but it's possible he could. My original idea for the move was using absolute zero to hyper-harden his fists but that would ruin his arms worse than One for All