I wouldn't turn the heater on and off. It's almost the same thing than putting your rabbit inside / outside and prevent him from adapting. Can't you just leave the heater on a low setting all the time? That being said, my rabbits are in a room inside of my house where it's not particularly cold and their ears are completely cold, like they are every winter. I found that rabbits' ears reflect the outside weather more than the inside temperature (and, weirdly enough, tend to get cold or warm about 24 hours BEFORE the temperature changes - they are a lot more accurate than the weather reports on TV ^^). My rabbits are free-ranged, if yours is too : I give them a cardboard box with two or three small openings and lots of hay in it. They like to be inside of it when it's really cold as it helps them feeling warmer. They also have a cushion and they don't use it at all when it's hot, but them seem to like laying on it when it's cold (I suppose it keeps their belly warm ^^).
On the plus side, rabbits rarely die because of the cold. As long as it's not freezing and that your rabbit is in good health, he should be fine.
:headsmack lol
