Reverse only after driving a while

My 92 Toyota Corona only goes into reverse after I have been driving it for a while (15-20 minutes). If you try to put it in reverse from a cold start it will not engage; the gear selector will go into reverse but nothing will happen (same as if it were in PARK). If you are driving for a while the care will go into reverse with no problem (100 percent of the time after warm). Or, if you are driving for a while then stop the car and go into a store or something, when you come out and restart the car, it will go into reverse with no problem. Even if you leave if for 30-40 minutes. This is a recently purchased used car. I knew about the problem before I purchased the car but the previous owner just decided to back in everywhere. Does anyone have any idea why this would happen? Thank you in advance.