Pete, I have the same Arcoaire furnace model #GUI075A012AIN that's about 9 years old.
Same cycling problem, occurs two or three times a winter season. I have found my problem to be the Flame Sensor. Remove the sensor, take a scotch pad or something similar, " light sand paper" and clean the discoloration. The annoying problem of heat going on and off for no reason will be fixed for about three months. This fixed my problem.