My blower runs continuously in Cool Mode with Fan in Auto mode. Unit achieves set temperature but fan continues to run. Selecting + 2 degrees above desired temp. will shut off fan.
Is the problem a blower relay limit switch? In heat mode it works OK.

Does the fan continue to run or is the outside unit running also at this time?

What is the model and brand of thermostat?

If the blower relay was defective the fan would never shut off in this case.

The blower fan continues to run after the compressor shuts down.
The thermostat control is a TotalLine programmable but there is no model # and I do not have the manual[second owner on house] Was installed in 1997. The compressor was replaced in 2006 [2 1/2 ton York] The air handler and thermosatat are the original installed in 1997. Handler is a Trane.

The fan will shut off it I toggle up a couple degrees above desired cooling setting. The unit is the second A/C in a second floor that is rarely used and the set temp is higher than normal [set on 80 degees F]

But the fan stills runs even at lower settings of 74-76 degrees. Did not used to do this so some component has failed or shorted.
Thanks