House blower and A/C cycles on/off (furnace, AC, heat)

[monomoy4]

Our AC compressor outside works fine when AC on....but with thermostat set to 'cold' and furnace/house blower to 'auto,' the blower cycles on and off without having reached the set temperature, yet. The compressor outside stays on and does not cycle. Compressor and furnace is an old Lennox (+10 years) system that otherwise works great and is maintained regularly.

Other thermostat setups and outcomes:
- Winter time with thermo set to 'heat' and blower to 'auto' = Fine with no cycling

- Temperature set to 'off' and blower to 'on' = cycling on and off

Ideas?

[M3 Mitch]

Possibly the interior blower motor is tripping some sort of thermal overload, problem with the overload or the motor has a problem causing it to draw excessive current? Check and see if the motor is getting hot. Use proper electrical safety precautions, if the motor has a problem it *may* shock you if you touch it, use the back of your hand rather than the palm.

Is this a heat pump or a furnace/AC combo?

[monomoy4]

It is a Lennox combo AC/furnace...I don't have the serial/part#'s with me right now, but it's an older model +12 years old. I replaced the Hunter digital thermostat with a new Honeywell 5-2-2. The old thermostat temp readings seemed off by about 3-4 deg F. The new one is accurate and works much better...only caught it cycling a few times in the 7 days since install. Could the fan limit control be bad?...or is that only a furnace-related issue?