We work on quite a few of these units at our shop, and warmer weather seems to bring out this type of problem. Typically they are fuel pump related. Do you know how to read fault codes on your set Assuming it is a later model 7HGJAB ? We find usually get a code 36 on these shutdowns, and fuel pump gets hot and stops pumping, or control board overheats and quits sending voltage to pump. Usually will start and run ok after everything cools off. Do not try to run with service door removed, thinking it will run cooler....will only make things worse.
we have relocated fuel pump on some sets, to cooler location, with some success. as far as cleaning, maybe stiff brush and shop vac, or some air pressure. Would be very careful with water around generator/control end, and you dont want to get water/ grease down on drive belt or pulleys