I would remove the radiator. Hold it up to the light. You should be able to see through the radiator if it is not clogged with leaves, dust, and cat hair.

I would use a garde hose to flush the debris out of the cooling fins- back to front. Direct the flow straight on. I would not use the high pressure car wash for this as lots of damage can occur to the cooling fins.

Shake the water out of the fins and hold it up to the light again. Rework those areas that retain any debris. Once you have all the crap out of the fins you should make sure that any that are bent over and restricting flow are carefully straightened.

With the radiator out you can direct the flow of the garden hose on the back side of the AC condensor and remove the accumulated crap that you will find there as well.

If you still have an indication that the car is still overheating at that point I would remove the instrument cluster and by pass the compensation board. That exercise will give you a more reliable gauge reading and you are liable to find out that the indicated overheating is simply caused by the comp board; a source of a variety of problems with the temperature gauge.

This image shows what to do once the cluster is out of the car. Good luck.

Randy