Check the voltage at the battery terminals during cranking. If it drops noticeably on a hot start, have someone use a load tester to drop the voltage to the same point and see what the current draw is. There's two possibilities for high current- - - -a dragging starter armature or a tight engine. You might try to turn the engine over by hand by grabbing the fan blades and turning it to check for tightness, but that's not a very definitive test. It's also possible the battery just isn't up to cranking a hot engine effectively.
Jerry

"It is better to be silent and be thought a fool than to speak and eliminate all doubt!" - Abraham Lincoln
Cringe and wail in fear, Eloi- - - - -we Morlocks are on the hunt!
There is nothing noble in being superior to your fellow man; true nobility is being superior to your former self. - Ernest Hemingway
Love your enemies and drive 'em nuts!