Plug and play so issue is most likely at furnace
BUT not knowing what it is doing and what it doesn't do makes it a guessing game.
Does it reach temp set point before turning off?
Does it attempt to run when temps drop......fan start, hear click of spark, main flame light at all?
Any lights on circuit board? Flashing green red number of blinks etc. are error codes.
Could be mis-positioned spark electrode, low battery voltage, dirty sail switch, bad circuit board, bad gas valve etc.
WHY did you change out thermostat?
Was furnace working correctly prior.....or had issues?