How much electricity does a thermostat consume?
Most thermostats use very little power, if any. Many of the Honeywell programmable thermostats you can buy from retail places, for instance, take 2 AA batteries for their power source and do NOT pull power from the fan unit. If your unit is a WiFi one, that may not be as true.

Either way, I'd be surprised to see one consume more than a dollar a month at most.