340 has a hard time starting when hot?

Does it have chrysler electronic igintion???

If so, check the reluctor gap in the distributor... .007" with non magnetic feeler gauge....

I installed a new elect dist kit once and didn't check the gap... It would start cold, but not hot... Turned out my reluctor gap was at .030"... Once I adjusted it properly, I never had a problem...

Also check Dizzy for side shaft play it will put your Reluctor gap all over the place. As they wear out it gets harder and harder to start. Happened to me years ago and New dist. fixed it.