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Those space heaters you have are probably too small. Get something larger.
No, it is not the landlord's responsibility to heat the unit. The reality is that reporting your landlord will piss him off and they can retaliate.
I've been using this De'Longhi Convector Panel Heater. A lot of great reviews, and it's pretty slim so doesn't take up a lot of room
So is something like just for show? https://www.amazon.com/DeLonghi-HCX9115E-Style-Convector-Heater/dp/B011OATNOS/ref=cm_cr_arp_d_product_top?ie=UTF8