[///Mposter]

Maybe it has nothing to do with the mirror but if you focused on two items that could be related . The transmission and car overheat. The radiator sometimes houses the transmission cooling and other times its in its own core housing. Either way, if the fan is not working , maybe it could cause the transmission to overheat, and the car temp to rise. Now the question is why only when the cruise control is on. Maybe there is a relay controller that is malfunctioning. Maybe there is a connector that is corroded and needs to be cleaned. Temp sensors are resistive, so check for shorts , damaged wiring harnesses , especially if its been in an accident or recently worked on. Also check for chassis grounds to be properly grounded. The motor sits on rubber mounts and needs those grounds to be good ( return path). That is all I can think of.