1990 Mercury Sable Heat stays on

The common problems here are the blend door motor and the control assembly. Problems of this nature require very specific diagnostic procedures to pinpoint causes. A shop manual is in order. You can usually find them on eBay for reasonable cost.

Of course, there is the "seat of the pants" method. For a start, I would try getting a used control assembly from a salvage yard. I thisk that should be your number one suspect.