WILL JUST SIMPLY SHUT DOWN

My COLD AND HOT METER ON MY 1992 FORD TEMPO STOPPED FUNCTIONING BUT MY CAR IS RUNNING SMOOTHLY TIL I DRIVE IT LONG DISTANCE. THEN IT WILL JUST SIMPLY SHUT DOWN. WHAT DO I NEED TO REPLACE OR FIX?

I recently purchased this car and found it functioning quite well
up til recently when the Meter for the Cold / Hot function on the left side of the dashboard stopped functioning.A few days later when I drove the car it would shut down after I drove it for a long distance of about 60 miles or more. What should I replace or fix to get the Cold/Hot meter functioning again so the car won't shut off after I drive it a long distance?

If I leave the car to rest or cool off it will start right up again if I leave it or cool it off for an hour or two.