You are fairly limited when living in an apartment.  A kerosine heater may work OK and be fairly economical.  We have had one for years (bought at a yard sale).  Does anyone know how long kerosine can be stored?  I have some that is 20+ years old.  I should dig it out and fire it up to see if it still works.  I am ashamed to say that I am not as prepared as I should be with that item.
I have heard of some propane heaters that can be used indoors, but do not have any experience with them.
I have used a fireplace insert as my main source of suplimentary heat.  It is a triple walled Buck stove with a thermostat for the fan control.  A marine battery and power inverter keep the fan running when the power is off.  When the battery runs out (hasn't yet), I can open the doors and put the screen in.  With the doors closed and the fan running I can heat the house.  With the doors open, I can heat the 12 feet in front of it.  I try to keep the battery charged!!   
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The Seeker