Put a thermometer on top of your fridge, and see how warm it gets there. Usually it's pretty warm with the residual heat coming out of the fridge, and since heat rises... It might be easier to just put your bottles up there. Personally I'd be nervous running a space heater 24/7 because of the fire hazard potential.
Bier war sein letztes wort dann trugen ihn die Englein fort...