After the thermostat reaches the desired room temparature, in the heat mode, the fan keeps going just blowing cold air, sometimes it shuts off, but after a while it will kick on with the heat still being off, can you please help me to identify this problem?

Thanks
Luis M.

On the circuit board there is a relay that turns the power on and off to energize the fan motor. There is a reasonable probability that the relay isn't opening reliably and keeps the fan motor turned on for a while until the relay finally opens.

You can test this by gently tapping on the circuit board relays with the handle of a table knife. Don't pound on it, just some gentle tapping that might cause the relay to open and shut off the motor.

If the tapping causes the motor to shut off, you will need to replace the circuit board.

I agree. Please let us know what you find.