Any reason for a clutch to get hot other than drag at idle from weak springs, or drag from the chain brake when it's cutting? Can a clutch actually slip enough during w.o.t. cutting to get too hot to touch?
Much like a car clutch, if the shoes and drum are worn, glazed(pressure plate and disk on a car), you can absolutely overpower the clutch and cause a continual slip that just makes it worse.
If you were to take a centrifugal clutch and bolt the bar on with no cover...and film it cutting with a high speed camera im sure you would see in the power stroke...that there is a bit of slip at ignition.
I'd pull it apart, clean it up with some brake cleaner, shoes too! smirch of lube on the bearing, put it back together. should be ok...
if the springs were weak you'd get the dingle, ring from the clutch when it was idling (I kind of miss that from the old saws...)
Not suggesting you are guilty of this, but main reason clutches get hot is because operators lug the rpm down to the point where the clutch no longer locks up tight and in some cases will actually stall the chain. If it's gettin hot it has been slipping. There's a reason why experienced operators are yelling at newbees to "keep the rpm up".
No lugging in this case, the saw has a distinct power band and will not cut well if you let the rpm drop, I let it feed itself with it's own weight.
I've eliminated any possibility of brake drag, and the saw can idle for five minutes without heating the clutch. The drum is new, so if it the clutch still gets hot next cutting session, I will have to suspect shoe wear.