The Doctor has left the cruise and was now on his way back to a specific junkyard. Low and behold, the TARDIS is there. He hides out until both the First Doctor and Susan exit the box to go inside it himself to finally chase after the Monk.
Cue Title Sequence: End?
Using the hair he used to run the DNA test from the previous, he tracks down the Monk and tries to reason with him.
"Why should I reason with you when you left me on that ice planet!"
The Monk then fights the Doctor, and gets the upper-hand (which I would imagine when a 34-year-old and a 17-year-old get in a fight), and soon, the Doctor gets into his old TARDIS and drags the Monk through the Time Vortex. The TARDIS, sensing the Monk hanging on, extends the shield around him. The Monk then does what no person should ever do and looks within the vortex.
Time goes through his head all at once. Everything that ever was and everything that ever could be is flashing within his mind at the equivalent of a hundred billion miles per millisecond. When the TARDIS lands, the Monk starts to convulse and spasm. Regeneration energy is blasting out of him at random intervals and he is bumbling random nonsense.
"It will happen, Doctor. The end. The end. The end. The end. The Institute. The Institute. It all happens...at the Institute. MENTAL! Escape. Escape. Escape. KILL ME! Spite me. End me. Help. Me. Escape."
He finally succumbs to the madness and regenerates. When it's over, the Monk has now taken the form of a baby Silurian. The Doctor notes the year, he's in (let's say, 1984), and uses the old TARDIS to go back to the junkyard in 1963, and waits it out, still as a statue.
Cue time lapse of the Doctor waiting in place as the world changes around him.
Cue the Doctor getting up, startling a couple convinced he was a statue.
Cue the Monk's final words replaying as the Doctor enters his present TARDIS
"It all happens...at the Institute."
Roll Credits: The Doctor Will Return in: Plan Z