The most likely culprit is the little blower fan that sucks sample air from the vent near the dome light, through a tube to the temp sensor. This fan should be running any time the ignition switch is on.
It is physically located in several different positions in the 124 chassis depending on year. Mine is behind and to the right of the blove box.
One way to see if it is running is to put a little smoke near the intake grill to the right of the dome light. You can use a cigarette (Yuck!) or some other source of smoke, maybe lighting a match then putting it out and quickly hold the smoking match near the grill. If it does not draw air into the grill, you will need to investigate.