The first thought that comes to my mind is a problem with the rings. I would, just for the heck of it, pull the injectors and pour some atf into the cylinders and let it sit overnight. The next day crank it over with the injectors out (to blow the excess out), reinstall the injectors crank it and see what happens. I don't really have an ideer as to why it works the way it does cold versus hot but I would at least try this just to see if it makes any difference.

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Jim