this might sound wierd, but it could be because the timing is too far advanced and the spark is igniting the start-up mixture too early and the combustion is stopping the piston half way up the compression stroke
when the engine is hot the compression is a bit higher because everything has expanded, maybe it starts OK when cold because of blowby on the pistons, but more compression when hot and it can't start it
of course, a crook battery would be affected more than a good one - so my theory, and a crook battery theory might go hand-in-hand - crap battery starts it fine when cold, but not when hot
ummmmmm
so I agree with them - crook battery, good timing, retard the timing will let it start but the timing will be crap, so replace the battery

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