I would check to see if you are getting spark when this condition happens
I have seen many fuel filters and most if not all appear to be empty even with the engine running .
If you still think it is fuel next time this happens try giving the engine a squirt of starting fluid the engine should run for a few seconds if it is a fuel problem.
Heat soak problems usually turn out to be ignition related, so check for spark next time.
Engine may try and run when it gets a little flurrie of spark too
Vapor lock went out in the ealy 60's
Ignition Switch An ignition switch with worn contacts can cause a loss of voltage to the ignition system and cause the engine to stall while driving.
Igniter An igniter that fails intermittently will cause a loss of spark and can cause the engine to stall while driving.
Engine Wire Harness An engine wire harness that has a poor connection or has a broken wire that is affected by road vibration can cause the engine to stall while driving.
Hot Air Induction System A hot air induction system malfunction in cold damp weather will cause the carburetor to ice up and can cause the engine to stall while driving.
Search didn't turn up much, my money is on the igniter
But you're going to have to do some testing to get to bottom of your problem.
The starting fluid will confirm your fuel theory.
Once you get it narrowed down to spark or fuel post back and I will try to help with diagnosis.