When your window stops partway up, the motor is stalling out against whatever is binding the window regulator/track/glide mechanism. The motor gets hot and trips the thermal overload protection. Once it cools down and resets, the motor will work again.
You'll need to determine what is creating the binding condition. Someone might have been in there before you and bent or adjusted a glass guide improperly; that could create enough drag to do what your describing. There might also be old collision damage that was not properly repaired.
