Hi JP,
Some questions:
Is it easy to turn over when it's hot? Easier than when it's cold? Or the other way around - really stiff to turn when hot?
Does it smoke at any time when running (and if so, what colour)? Is it smoking when it's stalling out?
Does it gradually slow down and stop, or does it just quit all of a sudden?
If you try to start it when hot, what does it sound like? Wheezy or normal? Do you get any white smoke?
I'm sure others will chime in with questions & suggestions that I haven't thought of.