2001 Accent starter doesn't crank when engine hot. New battery, new starter. I have to wait 10-15 min and there is no problem???

Was it running before you worked on it? If so, double check your work.
Make sure battery has a full charge and battery connections all good. Did you check good voltage and ground for fuel pump motor at the wiring connector?
If it cranks good but won't start, have a helper crank it, while you check for spark at the spark plugs. If spark everywhere, use a gage and check proper fuel pressure, I don't care if the pump is new, check fuel pressure, anyway. Also, check fuel injector pulse. Only crank the starter motor a few seconds at a time, let it cool off.
Are there any applicable trouble codes? How long since over-all tune-up?

Is the car engine turning/ swinging when the key is turned. If the engine is cranking then look at the distributor and the spark plugs and engine timing also it is worth a look at the fuel pump and supply to the injectors there should be a valve similar to the wheel valve on the injector bank press the valve with key on you should see fuel spurt out under pressure as the pump will be keeping the injectors under pressure . If the car is not cranking then look at the starter.

Sounds like a bad starter to me....the clicking ...sounds like the solenoid is throwing the drive gear out of the starter engaging the flywheel, but not sending power to the motor itself to turn the engine over.The battery getting hot suggest a "stuck or shorted" starter motor. The starter is a two step process.
Of course the extreme end could be a seized engine. Try turning the engine by hand at the crank ballancer bolt [clockwise only,battery disconnected] and see if it turns freely.

sounds like a bad starter

The humming would be the fuel pump coming on. It should only hum for a few seconds, then shut off.
Your problem is with the start circuit from the battery to the starter, or from the ignition switch to the starter solenoid. Check the connections at the starter (the big cable) for tightness.
Is the battery charged up enough to turn the engine over? Check by turning headlights on and observe while someone turns key to crank. If they dim a LOT, then either battery is too low, or the starter is bad and needs removing for testing. If brightness doesn't change, then the circuit from ignition switch to starter solenoid is likely not working. Check for 12 volts at the small wire to starter solenoid with key in cranking position. If you have power there, the solenoid may be bad. Remove starter for testing. If no power at solenoid in starting position, then either the ignition switch is bad or the neutral safety switch might be the problem, or the wiring from the switch to the starter solenoid is not passing current.
Good luck.

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If he installed a new or remanufatured starter, I would suspect a weak battery possibly. If he installed a used starter, I would say the starter is bad. A hot engine is harder to crank than a cold engine and if the starter is marginal it will act the way you described. Try boosting your vehicle the next time it's hot, or get your battery load tested by a reputable shop that doesn't sell batteries. I have had experience with remanufactured starters that were no better than the unit I removed from the vehicle. Have him get a second reman and see if that doesn't solve the problem.

is the security light on? Try ,crank it ,leave the ign. on for 1 min. Crank again,leave ign. on for 1 min.
should reset ,may have to do that several times.

Sounds like a bad starter to me. When starters get hot, they sometimes fail.

I'd check the key at the dealership. The battery may be flat in it. Also have the key code match to the CPU checked. The security may be the problem or it may be an electical fault such as sticky starter motor brushes or a dead segment in the starter motor amature.