Okay, I'll give a serious answer now.
I had the same problem in a Chicago apartment years ago. Actually, the whole front half of the apartment was freezing, including my bedroom, even after putting all that darn plastic stuff over the windows. The landlord was too cheap to do anything about it, so I did resort to using a space heater. As long as you never leave it on when you're not around, I don't think it would be a problem, and I think it probably is one of the least expensive options. I really don't know what other options you have. You could get a cat -- they're warm!