Furnace flames cycles off before temp is reached

First the flame WILL cut off before the blower on an RV furnace. this is so the furnace cools down

Second. Thermostats can be placed so hot air from the furnace hits them and "Fakes" them into thinking it'shot enough.. Check air flow to find if that's the case.

Third the T-Stat may have an adjustable "Anticipator" this device actually heats the T-Stat slightly in order to anticipate the residual heat in the furnace as it cools down. It may need adjustment. if that is it's adjustable.