Why would temp swing stress the fish? That is natural and happens in nature any day? Imho constant hight temp is much more detrimental for fish health than some temp swings, as long as they are within an acceptable range.I would leave the heater on, otherwise the tank could experience big temperature swings, which would stress the fish. It could also get too cold, which could kill your fish
In places like Thailand where the betta is from, the temperature is fairly constant.
It is much healthier for fish to have a constant temp than regular temperature swings.
Especially when you're not there, you cannot control how low the temperature will go, too low, and it could kill the fish.