My Sonata wont start when it has run for sometime but when it cools it start right up ???

Jose check the fuel pressure when the car is hot and up to temp, It seems to be fuel related.

Sounds like vehicle is vapor locking have vehicle put up on a lift and check to see it the heat shield is missing this is a piece of metal that goes between the exhaust system and the gas tank. If this is missing after vehicle heats up the heat from the exhaust will cause the gas in the tank to vapor lock.

Or worn bushings in the starter if they still have bushings some have bearings and if dry heat up and expand, Check fuel issues first.