I don't believe the heat soak is coming from the flywheel air. The air is spun from the flywheel directly up to the carb box. And many of the older series huskies have no carb soak issues. Bob
@Spike60 mentioned the carb being much closer to the the top of the cylinder with the laid back cylinder design as being the culprit. In fact the new 572 design has added insulation for this reason.
Terry's thought however of blocking off the air injection forcing more air over the cylinder fins is interesting. I think I would try running the Saw with no filter cover, and see if the issue goes away. Then try it with the air injection blocked off with no cover.
I would hate to cut up a cover and have the issue remain.