get an old-fashioned mercury thermometer
They’re also more accurate over months and years, than digitals
But yeah, heat and cold greatly reduce battery life. That said, we have an external thermometer that goes with our heat pump, to tell the heat pump when it’s cold enough outside to not bother trying, but to switch to the auxillary heat. It’s a whole different type of battery, lithium, designed for longer life out in the heat and cold. I don’t know if that type of battery exists in the size needed for the digital thermometers but you could check. They still need to be changed, but it’s about a year, not months.