I had the same problem with the 350 in my 52 sedan, hard to start after getting warm, it would always start but made me wonder if it would...............after dealing with this, getting a heat shield, a hot shot relay, my wife asked me to have the battery checked,I told her it was not the battery.....................I was wrong, got me a new battery and no more problems, the old battery had a dead cell in it..........I dealt with this problem for a yr and half.. wifes are smart..
may not b e your problem but .....