My car will shift fine but then all of a sudden it just stops and won't move

Hello, 5 speed manual or automatic? If the vehicle has a manual transmission, the chances are that you have a clutch issue, and when it gets hot you are losing friction. Inspect your clutch, and make sure not to rest your foot on the clutch pedal while driving as this will result in even more heat. How far from fully released on the clutch pedal before the clutch actually engages, and you feel the car start to move? If the clutch only works for about 1-2 inches of pedal travel, likely needs replacement. http://repairpal.com/hyundai-within-10-miles-of-marietta-ohio-45750