Usually, if the sides of the unit is very hot, or abnormally hot than usual, the condenser is not giving off the heat generated by the compressor. Usual problem for units with a condenser fan is that the fan stops turning. So, if you have a fan at the back of the unit, please check this if it still running.
Then in some cases, it could also be a case of a dirty condenser coil. The condenser coil is the one being cooled by the fan, so if the fan is running, then the condenser coil could be dirty. Please check the air inlet of the condenser because this is where the dirt would accumulate.
The motor that could be shutting on and off once you open the door is the evaporator fan motor. This prevents the cold air from being blown away if the doors are open so it stops when ever any door is open.