Shifting Issues:
Check the shift and select cables movement {lubrication} or/and the shifter in the console.
Coolant Temperature:
Did the radiator fan turn on?
IF the coolant temperature gauge is 'correct' - then the warning switch sensor is failing. {GM 25036809 / AC Delco 213-71 / Standard Ignition TS-168 (Aftermarket: Delphi TS10051)
If you’re in doubt about the ‘health’ of the coolant, completely flush the system.
As you're draining the coolant system, I suggest replacing the engine coolant temperature sensor for the ECM as well {GM 25036979}
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Original Owner of a Silver '88 GT
Under 'Production Refurbishment' @ 136k Miles