I don't know for thermostats, but I chose February 29 as the date at which I replace my smoke detectors batteries (yes, once every 4 years!) and I have never had a smoke detector fail to let me know that I burned my toast. I use Duracell or GP Ultra batteries. Thermostats might draw more current than smoke detectors, you would have to experiment how long they last.

I don't replace my smoke detector batteries until they chirp an alert.

The (WiFi) thermostats at work take two AA batteries, have a battery condition icon on the display and also report the voltage reading and condition via the app. I don't replace them until the condition indicates a need.

My non-wifi thermostats have an LCD display which shows the temperature. When the batteries dies, that display goes blank - that's the only indication. I have two wifi thermostats which don't have batteries.

I think it is overkill to replace batteries in a hard wired smoke detector every year. The battery is only used when the power fails. The battery should be good until the date code. A Duracell 9v alkaline battery has a 5 year shelf life. The smoke detector should warn you if the battery is beginning to fail.

What is the model of your non WiFi thermostats? Having no battery indicator is a bad design. Even the Honeywell RTH2300 thermostat, which sells for $24 has a low battery indicator.

I'm not sure how costly it could be to replace a handful of batteries.

I've had two not-inexpensive Honeywell Redlink thermostats for about 3 years. I think they were ~$150 each - I bought them from Amazon at my HVAC contractors suggestion, the Amazon price was cheaper than what he could sell them to me for.

They have a 24v power connection from the equipment they control and also have batteries. The batteries seem to last a bit less than two years and signal it's replacement time by flashing the display. There's no other battery indicator.

The battery in my thermostat is only for power backup. I checked it once after 5 years, it was still good, but there was corrosion on the terminals.

mike c, I think I'd read that's what mine were for too, but maybe not. All the same, they needed to be replaced.