I have a Kohler 4 kw single cylinder in my motorhome. The exhaust pipe on mine was 1" steel pipe with one swedged joint in it. The OD of the swedge was 1-1/2", so I just went over to AutoZone and asked for the smallest muffler they had that fit a 1-1/2" pipe. They don't list them by size (of course!), so the guy just kinda threw up his hands and said they couldn't do that, but finally got him to bring out the smallest muffler box they had and let's take a look, hit it on the second try, was for a Toyota, don't know the model, but it's quieter than the old one was and you just cut the generator exhaust pipe off leaving the swedged joint and it connects right up with standard sized pipe. It's 12" long, 8" wide and 3" high, more or less, a normal oval shaped car muffler.
With mine, it seems that the motor/generator unit itself makes as much, if not more, noise than the exhaust once a muffler's on it - so the muffler's only half the battle. Fiberglass ceiling tiles in the generator compartment help some. I'd imagine that yours has a big centrifugal fan on it, so not much worry about the heat.