Most covers are ABS and hopefully white. ABS has a max operating temperature of 176F. If they are melting, they would need to be getting hotter than that.
The source of heat is the condenser coil which normally runs ~130F. If the condenser coil is over temperature and cannot reject enough heat, that would likely caused by poor airflow. Poor airflow can be caused by 1) clogged condenser coil fins or 2) low fan speed. Since the blower motor for roof A/C drives both evaporator and condenser fans, (usually?) you should be able to know if the evaporator fan is not running while standing inside. It is remotely possible the fan blade is damaged or loose or fallen off, or loose on the shaft?
Retired Mechanical Engineer (MIT)
Design/Manufacturing Engineer Manager
Former Safari Motor Coaches plant engineer