Elena doesn't spend too much time thinking about him; she knows that if she started, she'd never stop. Elijah strikes her as the type of guy that a girl could lose herself in, and she vows that she will not let him do that to her. And somewhere along the way, she even manages to convince herself that he hasn't already done so.
If she did think about it, she'd decide that her not thinking too much about him is exactly what led her into this mess in the first place. Because, had she thought about what she was doing, had she bothered to analyze her actions, she'd of realized how monumentally stupid it was for her to let him anywhere near her.
But, because she doesn't allow herself to think when she's around him, she doesn't tell him to leave when he comes in her room, doesn't tell him to stop when he kisses her, doesn't tell him how wrong it is when he's taking her clothes off. A part of her doesn't care that it's wrong. A part of her likes the wrongness of it all because it is exactly who she once was, before Stefan and Damon and vampires and car crashes and dead parents. Before life became a fight for survival. (And maybe she feels he's her last real vestige of protection, because he's the only thing keeping her from being sacrificed by Klaus.)
When she's with Stefan, she keeps the memories of Elijah locked safely in a corner of her mind where Stefan can't touch and when she's with Damon, she makes sure the walls are up extra high. She suspects Caroline knows because she sees the looks the blonde shoots her, a mixture of jealousy, disgust, and satisfaction.
Then Elijah will visit and nothing else will matter because he pushes everything from her mind until it's just him; and she refuses to think about him, so she's a blank canvas he can mold and paint whatever he wants on, and she lets him because...
To be honest, she's not sure why she lets him. There's something about him that seeps into every pore of her human body, practically ingrains itself in her DNA. Like a drug, she's hooked and she's not sure why and she's not sure she wants to know anyway.
So she doesn't spend much time thinking about him. She avoids his eyes, focusing way too much attention on his mouth instead, and vows never to let herself get lost in him.