Question Regardling Light-proofing

Actually, I lied. This question isn't really about light-proofing, its about insulation. My apartment is too damned cold and I want to stop all the heat from going out the window. (Along with the money I'm presently paying to generate said heat.) My proposed solution is to tack up a blanket or two over the window to help hold in heat. That's where light-proofing comes into the equation: I know some of y'all have done and/or are doing similar to keep light out of your bedrooms. So, can anyone recommend the best way to do this without needing to employ nails? I rent and putting nails into the walls is not a good idea. Plus I'm not actually sure I can... I'm in a basement apartment and I get the feeling there's not a whole lot of wall-space between me and the cement or bricks of the building's foundation. Trying to put nails into concrete covered by a thin layer of stucco or whatever is not going to be happening. So, any thoughts?

This will also, incidentally, be a boon to certain migraine-prone folks I will be having as guests in March, to protect them from the wicked daystar. So I'm sure they will thank you too if you can help me out with this. :) And that brings this all back to light-proofing. ;-)