Sounds like it was getting very close to vapor lock. Keep in mind that state change is not a linear process, it's a threshold effect. Once you get to boiling it's all over, but just below that it can be fine.
OK, but that is exterior surfaces. The heat source is inside (cylinder, muffler). One could make the argument that if the saw is hotter outside it's doing a better job moving heat from inside to out. You would indeed need a temperature measurement of the carb to be sure. I think the evidence is that it's probably hotter inside, but it may not be as extreme as it seems from touching the case.
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I wonder if the strato air inlet acts as a heat duct to bring cylinder heat to the carb area? With a non-strato the carb is connected to the case, which will be cooler and have fuel. The air inlets for a strato connect to the hot cylinder to the air valve, although that is supposed to be closed. I have not noticed that my GZ4000's are any more or less prone to vapor lock, but it is a different design where the air valve is bakelite and part of the carb mount.