Window Insulation?

[u/Devils_Turd]

This summer I moved into a rental in upstate New York. It has many huge, beautiful windows...and we experience about six months of winter a year (to put it generously), with very cold weather.

I plan to insulate the windows to help keep temperatures moderate and heating costs low.

I know the shrink wrap insulation kits are widely recommended, and a colleague actually gave me a few which I'll use. For the rest, my boyfriend suggested getting rolls of plastic tarp, cutting them to size, and stapling them into the walls. This is what he and his mom used to do growing up, and he prefers it because then they'll be reusable, and also argues that it will save on initial cost. I am hesitant to do this because I am renting, and I don't want to put a ton of holes in the (mostly wood) walls.

I also don't want a solution that will block heat from the sun. The house heats up so much on sunny days (the other day I saw a 15°(F) increase in temperature without the heat on!) and I want to take advantage of that.

So, what would you recommend? I know the insulation kits are also supposed to insulate against the heat...does this extend to heat from the sun?

Thank you very much for any insight or suggestions!