2007 Camry not cranking after being driven

Computer controlled charging system. You need a shop that knows how to check the system out properly, not just component testing. I have seen some of these have what is called a flying open, when the alternator reaches a certain RPM a circuit goes open and the alternator drops the charge rate. Don’t know if this is what you have but it warrants getting checked.

A multi tester is useful for trouble shooting such things . Sounds like a cable supplying the starter gets hot and creates resistance , Pos batt. cable may go to a junction box before reaching the starter , A voltage drop test may have to be done if nothing else is found

My book says 3 things for a hot engine that won't start. 1.Air filter clogged. 2. Fuel not reaching injector system. 3. Battery ground side issue. It's hard to tell if this is a genuine fuel related issue (like a clogged fuel filter) or an electrical issue like a bad connection at the starter solenoid, so if you still have no idea and you don't have any DTCs, it's time to get the multimeter and tool set out. I genuinely hope you do this diagnostic yourself or with a friend b/c mechanics can have a field day with you on something like this. $$$$