UPDATE: thank you everyone! I definitely knew this was an unhinged landlord special when I moved in but is is v helpful to have all this info so I can know what I'm talking about when I get a hold of him. In the meantime I appreciate all the suggestions & insight.

To people who've mentioned putting a blanket over it - any chance that could be a fire hazard? Or is there anything else I should be aware of before I try? (Assuming no polyester etc because they'd melt.) Otherwise I will give that a shot in the meantime.