If you don’t need both window units remove one.
Close up the fireplaces and pur clear plastic kits over the windows.
Use the space heater when you are out (MAKE SURE IT IS SECURE FROM THE PETS) and when you sleep.
Do you have a lease? It may say landlord pays heat since he did at first.
I had a lease that said the landlord provided heat, but they arbitrarily decided to rewrite it without heat and raise my rent last year.
I THINK that they have to provide a method of heating that is controlled by a thermostat, which I do not have. I also think this requirement might have to do with it being a multi-family dwelling and not a stand alone, single family unit.
Every time I call the city, they have no idea that this house has 5 separate units in it...