Hi Gary, here how I see it
Your large gasser is normally equipped with a main engine in exes of 300 HP, your gen.set is probably 10 HP. Running the gen.set on the road, will only take the amount of heat, generated by the extra 10HP (dash AC), from your radiator. this amount in just 1/30 or 3.3% of his cooling capacity. Normally, with dash AC the fan would work 3.3% more. Is your cooling system in good condition Gary?
The heat generated from the AC, has nothing to do with the main radiator, well, I think in US just like on the old continent, dash AC has his own. radiator.
Greetings from Antwerp