Is it truly overheating or are you reacting to the gauge going into the red?

I had this on my '86, and brother had it in his '89.

If it's merely the gauge (versus boiling over), then it's likely to be the compensating board. The comp board is installed into the cluster PC board, but you must dismount the PC board from the cluster housing -- 7 screws. The first picture below shows where the compensating board fits.

The second and third images give you a close-up of the area.

Often (but not always) resoldering the comp board and cleaning and tightening the 4 connecting pins solves the problem. To tighten the pins you can gently, carefully squeeze the female connectors (on the comp board) so they grip the pins (on the cluster PC board) more tightly.

If this doesn't help, you can certainly find a replacement board, perhaps new from the dealer $$. For my car, I replaced the IC and transistor on the board. That solved it.

Another approach that others have used successfully is to eliminate the comp board by bypassing it. You merely connect two of the four pins -- I don't know which two, but it's in the archives.