First, as Jeff mentioned, make sure your coolant level is correct and make sure there are no air bubbles trapped in there. I think if you search this forum you'll find instructions on purging air from the system.
Second, if you're certain your coolant level is right and you have no air bubbles trapped, go ahead and replace the thermostat. Failure of the thermostat is a relatively common occurrence; replacing the thermostat is a pretty cheap and easy do-it-yourself job.
'83 240D, 252k miles