I think you're onto something with the on/off timer...
however, Daox's idea is probably the most efficient due to the randomness of the weather. There is no need in freezing the pipes because you set the timer off for too long and there is no need to heat the drafty garage by leaving the timer on for too long.
I think the problem will come from not having a remotely operated thermostat for the wall outlet. You'll have to build your own, or do a deeper google search than I did
It sounds simple enough though. Set a thermostat to a relay to allow power through the outlet.