Running gen while on the road

Leave the door on in hot or cold situations. Bypass the fuel pump with an external one located out of the genset compartment.

And, running the genset with roof air is more economical than the dash air also. A side benefit is once you arrive at your destination, the entire coach is cooled, instead of the front area, only.

(I was a RV tech for almost 10 years)

Onan indicates in my manual not to run the generator without the cover because it will run hotter. Onan has had some problems with fuel pumps getting too hot. My fuel pump was replaced under warranty. If I encounter another problem with my Onan fuel pump I am going to move it over to the MH frame where it will stay cooler. The Onan repairman told me many of the generators are sold as complete units so Onan puts the fuel pump on the generator where it gets too hot. The Onan gererators are not built just for RVs. The code thrown by the generator should indicate if the generator has a lacking fuel problem.

I installed louvered vents in my bin door that houses the gen and no more issues. I used basic white floor vents and it looks factory.

With all the issues these have with overheating to me it's a design flaw. Why manufacturers continue to put gens with little ventilation directly behind the motor and headers is beyond me. It's literally the worst place you could put it - or the best place if you are trying to get overheat shut downs as frequently as possible. I seriously think some of these engineers have never spent a day in an RV.

If the genny is an Onan, the manual states not to run it without the cover.
If it is shutting down due to over temp it should giving a code indicating so.

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.

Rookie Rver :C here! Yes, taking the cover off will definitely improve, if not solve the problem. The generator needs to breath....breath a lot. I run mine all the time while traveling with no problem. When parked, if there is little to no wind is when the generator may automatically shut off. When running generator while parked in driveway with little to no wind I now plug in and place a fan near.