I would like to add something to this good list of things to check. On your model I don't know where the interior temp sensor is located. But find it and ensure that the air tube that provided interior air to the sensor is not deteriorated, collapsed or otherwise blocking air flow to the sensor.
Additionally, I don't think your car has one, but on the 124 cars there is a small fan that feeds air to that sensor. This fan runs any time the ignition is on. If it is worn out, it will cause similar problems.