I had the same problem with my '51. Would start great when cold but when hot would not turn over at all. It was the ground cable connections that had corroded. Heat results in more resistance and if you have a marginal connection the additional resistance when hot causes the problem. Clean all of your battery cable connections and see if that helps.
Kent

1937 Chevy 1/2 ton
1942 Chevy 1/2 ton
1947 Diamond T Model 509
1951 Chevy 1/2 ton
1950 Chevy COE Model 5700 ~ "Barney" ~ And more pix