I will share my motorcycle experience with what you are doing.
I had a Honda 100 CC motorcycle in about 1974. It had a black coated aluminum finned cylinder.
You could not ride that bike with shorts, the heat radiating away from that black cylinder would cook your legs.
In 1976, I bought a 125 Yamaha, almost the same bike, but, a little bigger displacement.
(I rode it to class up at Hokieville)
The Yamaha had a shiny aluminum cylinder head,,
there was ZERO issues with riding in shorts, as the shiny aluminum did not radiate heat.
DO NOT touch that cylinder,, the temp was so high that a simple touch would remove your skin RIGHT THEN!!
I think the Yamaha survived, because at the higher cylinder temperature, convection removed enough heat.
Painting the cylinder black only helps if the cylinder fins are facing something cool.
It would have zero help, if the fins are facing the muffler.
It would be best if the fins painted were facing outer space,, then the fins think they are radiating to absolute zero temp.
It would do no good, if the saw were then turned on its side.
