Broken Window in private housing

I moved into my apartment and the window was broken and the inspection people must have missed it. For context, one of the window panels are completely broken, there broken glass where the panel should be, it’s also completely off it’s hinges, so when i open it it would stay open, and it doesn’t even stay closed, if you slightly pull it horizontally, it will come off. This has been broken since i moved in, so about 6 weeks and my house company (Green Street realty) has been trying to fix it but its a long process because the window has to get replaced.

But this month the electricity bill came out to be over 200 dollars for a 2Bed1Bath! But i know for a fact is because of the broken window, because the temperature isn’t getting regulated at all, I have no idea what to do because it’s a lot of money for the electricity bill, is it possible for Green St realty to reimburse me?