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The most likely cause is going to be the fuel pump, it is not unusual for them to be intermittant like that and to work better when cold.
It is probably just barely able to supply enough fuel cold and then as it warms up it gets worse.
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It definately can, it it a little uncommon for them to only do it every time it warms up.
I would start with a fuel pressure test and if that checks out then I would replace the coil.