Running gen while on the road

Taking off the generator cover will probably make it run hotter. Perhaps you are not getting the airflow around the generator that it requires. Look and see if there are any obstructions outside or inside the generator cover. Critters have a habit of building nests under generator covers. Also make sure that yu have the right weight oil for the outside temperatures.
If that doesn't do it, you can put a louvered vent on the outside of the RV access door that directs air on to the generator as you drive. I've never seen anyone that had to do that but maybe your coach is different.