Starter will not crank when engine is hot

It sounds like your starter motor is bad. As temperature rises so does electrical resistance, and when the starter brushes are worn and have high resistance already you will in turn have the click but no start concern. It can also be cause by a battery cable or terminal that is corroded. Also, verify you have a good tight connection at the starter. And of course good battery voltage. I always eliminate the easiest items 1-test battery, 2- verify and or clean terminals, 3- verify connection at starter 4- while at the starter connection verify good voltage to it. 5- voltage drop test cable. These are just my procedures as I am a flat rate tech and I need to be fast and accurate.