He cracks me up, and whenever he came up with one of his insults I’d probably laugh in his face and ask for more. I’m pretty sure I’d get along as well with him as anyone might, and when necessary, I can withdraw into a more or less impermeable little semi-catatonic world, for hours on end.
The OP, however, mentioned a stipend, so a stipend I shall have. Fifty grand a year sounds fair, so make it a hundred.
I hang out with guys like Sheldon for fun, anyway, so no problem, just pay me what I make now anyway, maybe a bit extra (so let’s say $100 000 for a nice round figure) since looking after Sheldon would be a full-time job really. HOWEVER Section 8,subsection C, para 4 will need to be excised from the Roommate Agreement . I can put up with a 30 minute warning, no more.
It’s funny of all the guys Sheldon is the only one who respects a woman’s intelligence IE Amy and Leonard’s mother. All the other guys show real contempt for women and are obsessed in banging a hot chick, even Leonard “the good guy” was obsessed with Penny only because she is hot and hot girls usually don’t pay attention the guys like him. So, Sheldon respects women the most.
An annual million dollars would make the seething hate sting much less.
No money. Just regular sex with Penny.
I’d do it for the luxury and pampering, no monetary compensation required. Sheldon would get annoying at times but would be an interesting roommate. He’s the ultimate geek, and we like a lot of geeky movies, television, books, video games, etc, so we’d have that in common. Aside from some verbal insults, Sheldon isn’t mean spirited at all, has something of a sense of humor, and can be generous. And of course he is incredibly knowledgeable about a wide range of topics (except for human interactions, where he is incredibly naive).
Requirements: My wife must of course be included in the living arrangements. Sheldon MUST honor the “do not disturb” sign we put on the door during coitus :D. We both love Mexican food, so he’d have to be able to eat it or at least find his own food when we make it.
The question would be if Sheldon could tolerate living with us 
While we’re into many geeky things, and have an interest in science, my physics knowledge isn’t much more advanced than Penny’s, and my wife even less so. So most of his physics based expositions would go right over our heads. I’d be willing to learn though.
I’ve had worse roommates.
ETA: And I suppose they have, too.
What are you talking about? Pay me? Just whatever it takes to cover his rent. He’d be a great housemate.
(I assume we’re not sharing rooms here… “roommate” is just Americanese for housemate or flatmate, right?)
Actually, on second thought, I really should’t be sharing with him. After the unpleasantness of 2007, I’ve made it a policy not to share houses with people I’d like to be in relationships with. We’re not going down THAT path again.
Sorry dude, but one of the things I was going to ask for is Leonard, and apparently he’s suffered some sort of serious mishap…
(Monkey Chews, while roomies may share rooms, most often and definitely in the case of Big Bang Theory, they’re exactly the same as flatmates)
One factor needs to be clarified. The roommate agreement clearly states "Roommates agree that Friday nights shall be reserved for watching Joss Whedon’s brilliant new series, “Firefly”. " Does the Universal Library make this possible?
Since I am pretty much a female Sheldon, give me enough to live on and I’ll do it.
As a true nerd that only thinks of science and sex, I vote this post wins. Nerds do get a lot of sex too, just so you know. Penny would be payment enough for me and Bernie once in a while, she’s cute.
Here come the masturbation jokes…
I’d alternate between Penny, Bernie, and Leslie six days of the week and keep Missy for Sundays … wow! 
Insert appropriate flirtatious remark here.
It’ll have to be a PennyBot. RhI doesn’t employ human sex slaves, and anyway I can’t risk exposing Sheldon to the real Penny again lest she ruin the project with her squeamishness.
It mystifies me why you would desire the amorous attention of a Penny Unit when a Bernadette unit is available, so I will include a free head CT in the deal.
So we’re clear: You are on the Short List DESPITE being a female Sheldon, not because of it.