Transmission will not shift into any gear after driving for fifteen minutes

When I drive my car the transmission would shift into second gear but hesitate to shift into third. Also after I drive the car for about fifteen minutes or more the car will not shift into any gear nor will it go into reverse. After the car cools down and I start to drive again the car would go into reverse and shift gears again but once the car heats up again nothing happens until the car cools again.