Check the battery terminal voltage during the hot start problem. If it drops below about 9 volts with the starter engaged, try a different battery. If the problem persists with a known good battery, it's time to look for internal engine problems that are causing the rotating assembly to tighten up when the engine is hot.
Cold cranking voltage with looser engine clearances should be somewhere in the 9.5-10 volt range, and you should be able to crank the engine for 15 seconds or so with the ignition disabled without a noticeable slowdown of cranking speed. My best guess is a battery with limited cranking amps and/or a compromised reserve capacity.
Jerry