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That's annoying!
I'd start by having a look at the spark plugs to be see if they're nice and clean on both pots.
Fairly cheap and very easy to replace, so a good pace to start.
Things that are effected by heat can be coils and windings. Not sure what makes the spark on those models, coils, igniters or whatever? but the crank position sensor would be a suspect and can fail when hot.
An outside contender could be plug caps or HT leads?
This is a tricky one as the fault is not actually stopping the engine but rather seems to be heat from the stopped engine migrating into something that is otherwise cooled.
( hence my thinking crank position sensor.)
Going on from that my last thoughts would be a temperature sensor? (I think you have two oil temp sensors and an ambient air temp sensor, it probably isn't the latter.)
Can you read any fault codes?
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