Thermostat White-Rodgers 1F82-261 switches to stage 2 heat for no apparent reason

I didn't look up the manual but it is very possible that it kicks in second stage after a set amount of time. There should be a installer configuration section where you can adjust those settings.... Now I'm curious, I'm going to look up the manual.

Some digital programmable thermostats are intelligent in that they determine the best way to get to point X in X time, I had a fellow who set his thermostat for X degrees at 6 am and he heard the furnace kicking on earlier than this time sometimes as early as 430 am. I checked out the thermostat and found it had something called "adaptive recovery" that determines the best way to reach the temperature setpoint without using the heat strips which is 2nd stage heat, this involves running the unit before the time set to most economically reach the setpoint at the time programmed, in other words it starts early to actually be at X temp at 6 am not start heating at 6 am. Since it ran before and still does other than this 2nd stage initiation it is the thermostat doing this most likely, I would thoroughly read your thermostats programming instructions or call the 800 # for the manufacturer of the thermostat, it is very likely doing what it is set up to do and there is nothing wrong.