How much are you willing to spend?
$30 USD solution
I use a single oil-filled electric radiator from Lakewood to heat my trailer. It doesn't do a whole lot if the temp goes very far below freezing, but that's because this trailer is old and not very airtight, in a fairly tight apartment or house it should do fine for a room or two.
$75-150 USD solutions
If you want some serious heat, get a propane cylinder(filled of course) and one of those Redyheaters that you see on the sidelines of NFL games. Scratch that, get one that a contractor would use, anything that says 100,000 BTU on it. A single 20lb cylinder should operate it for a couple of days anyway. They also make passive radiant type burners but they are less effiecient, usually burning up a cylinder in a few hours.
You could also go with the old standby, kerosene. A good kerosene heater should go for around $150-200 USD and burn for 10-12 hours on a full tank. Just make sure you don't damage the wick too much trying to figure out how to light it. Kerosene kind of stinks too.
Bottom basement, you should be able to pick up a fan-forced electric for $20-30, with quartz elements(far more effiecent) for $45-60 USD.
Also, call you're landlord and make sure he knows the heats out.