I should note that I brew in my kitchen, using a gas stove. Once I get to the temp I want, I can turn the gas flame down to a "maintenance" level for as long as I need to hold that temp. I'm not sure how easy it would be to do that outside on a propane burner, or with an electric heater setup for that matter.
I have not had good luck trying to maintain temperature on an electric coil stove. It seems like the coil continues to give off a lot of heat even after the coil is turned off. I always seem to overshoot target temperature if I shut off the burner at target temperature and leave the water on the burner. There's probably a certain number of degrees below target that I should shut off the burner to stay at the target temperature but I haven't figured out what it is.