2001 Chrysler PT Cruiser Over Heating

Is the check engine light on? Thermostat ever been replaced? and ECT(engine coolant temp) sensor can be bad without setting a code. With 101,000 on your engine, checking the timing belt is a good idea. It will only fail to turn the water pump if it breaks.

It seems to overheat only when the air temperature gets above 85 degree's. However, this is when you want to run the Air Conditioner. Is there something to look at that when the Air is running would cause it to over heat. When I run the Heater, it does not.

Two most common are 1.) Does the radiator cooling fan come on when engine is hot? And it should start with the A/C turned on reguardless of engine temp.
2.) Stuck thermostat, less comon because it should overheat, or fail to give heat inside when cold outside.

Yes the fans run with and without the AC on. They come on and go off as they should. I have replaced the radiator cap,thermostat,Flushed replaced the water pump. I have over heated But if the Head Casket was leaking would I not over heat no matter what the air temp is. No problem this last Fall or Winter.
This morning I drove to work 7 miles it did not get over 1/2 on the gauge Air Temp 72 degree's no AC on. Yesterday drove 7 miles with the AC on Air temp 85 degree's and I over heated.
Going home from work to night 62 degrees air temp I drove 5 miles with the temp gage at 1/2 I turned on the AC and 5 more mile then the gage started to rise to 3/4 and the car started missing more. It also seem to miss more with the AC running than not. Turned off the AC and the temp gage held at 3/4 for 2 miles. At home I sat at idle turned on the Heater and the temp gage dropped to 1/2.

Have a look at the fins of the radiator and A/C condenser, they could be clogged up with road grime, get a long air wand and blow out the radiator, then turn wand around and do the same to the a/c condenser. Not enough airflow!