I would start by replacing the trans fluid. Castrol Transmax import-multi vehicle. Drain it out of the bottom, refill through the small opening that is on top of the sheet metal cover that is on the front of the transmission. Put in seven quarts. It sounds as though the electric valve which opens and shifts to reverse is gummed up and doesn't move until the fluid is warm. New fluid may help, if not, transmission repair shop as this is a complex gearbox with no tolerance for error.