When I lived in South Florida, I kept a row of 4, 10 gallon unheated tanks in a screened-in porch.  When a cold front would come through, I would cover these aquariums with a quilt.  The only fish I ever lost due to cold were some Cardinal Tetras.   Some nights in the "winter", the air temperature would drop to the 40's or lower.  The tank's water temperate would often drop into the 60's.  I even raised some Dwarf Gourami's who are supposed to be very sensitive to air temperature in these tanks.

I see no reason why you would need a heater in a properly heated and insulated house.  The exception might be if you are keeping a very sensitive species.   Another reason might be to spawn a temperature sensitive species.  I have a heater only in my 55 gallon tank and that is because the Jack Dempseys don't seem to want to spawn at "room" temperature.  They can be kept indefinitely at "room" temperature, though.

I am speaking about freshwater species, since I have no experience with salt water tanks.  Those with salt water tanks are best to get their information elsewhere.

I feel that the requirement of an aquarium heater is largely propagated by the industry itself, in order to generate revenue.  Don't bother buying one, unless you have a specific need.