I have the Rheem Criterion II furnace. It is working OK. But the blower comes on after the desired temperature reached or it was turned off after a while.However, eventually it will turn off but blows cool air. I just don't know what to do because it blows the cool air. So I shut it down manually by turning the switch.
Will be appreciated if someone can help me to figure it out what issue is?

Regards,
Mike

"Blower comes on after ...temperature". Are you saying that the house heats up without the blower and then the blower comes on, or that the blower keeps running after the house reaches temperature and blows cold air? If it's a cold air issue, I'd reset the "fan off" switch to a higher temp. It should be going off above body temp or it will always feel cold.

Thanks for your response. I mean when the house reaches the desired temperature. The blower stops. It then pause
A while starts again but no heat just cold air. It comes on even I turn the furnace off on the thermostat. It eventually stops.

OK, that clarifies things a bit. A heater blower does not function through the t'stat unless you turn it to ON. In the auto position, the fan limit switch controls the fan on and off. What you are describing usually occurs when the fan OFF limit is too high, an usually more prevalent on very cold weather. The fan goes off, residual heat from the exchanger heats up the plenum and then the fan comes back on. On the front of the heater plenum, under the front cover, is a switch that is usually marked with 3 pointers-High Limit, Fan ON and Fan OFF. Move the fan OFF arrow a bit lower so that the fan will run a bit longer before shutting off. That way the plenum shouldn't heat soak and start up again. The fan switch would be set to come on at 125-135 and go off at 100 to 105 degrees. This switch may have to be fine tuned to keep the fan from coming on during summer and to keep the fan from short cycling during normal operation.
Your heater may be different but almost all function that way, particularly older units. Let us know how things work out.