When the motor heats up the transmission starts slipping ... anyone know a fix? on 2001 Lincoln Continental

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The issues only occurs once the motor heats up ... after about 20 miles of driving the check transmission light comes on
(2) Answers
probably a P1744 code or something of the like...from my research and first hand experience with this type of transaxle (front wheel drive/V8 is retarded concept, and transaxle was poorly manufactured/engineered to boot), your transmission is probably dying. If it has over 100,000 miles on it...and if you havent regularly flushed the ATF with Mercon V, AND replaced trans fluid filter inside pan, it is doomed.
If fluid hasnt been flushed ever, it is too late, dont flush it...but it would be wise to drop pan, change filter, and top off with Mercon V ATF.
The internal parts of transmission were poorly crafted by our friends at Ford...where there is plastic, there should be metal, and where there is metal, its cheap metal, such as the main oil pump splines, among other things. Lots of the solenoids inside the valve body had to be redesigned, because the original solenoids suck.
The only thing to do is get it rebuilt by a quality technician, or purchase a remanufactured unit with all the poor engineering flaws upgraded. Or go to the junkyard, get a used 4F50N transaxle for $650 or so, get it running, and sell it.
Or just change the filter for now, and hope for the best