A sensor out will turn your "check engine" light on. Those are relatively easy to track down.
ALMOST ALWAYS when a thermostat goes bad it will lock open and the car will be slow to warm up. Never saw an overheat problem caused by a bad thermostat, but of course anything can happen. More likely you have radiator blockage, either on the outside or inside, try a good radiator flush first. The suggestion that you may have a vacuum leak is a good one. You need a good trouble shooter to take a look/listen to it! If you drive up to the dealership he will charge you about $3500 for a transaxle rebuild or exchange.