Every time I start car it won't go into drive unless I go very slow

When I start car and go at normal speed it won't shift into drive unless you drive at approx 40 miles an hour for a couple of minutes. It sounds like a lot of pressure on engine before shifting. It's automatic. It does it every time I start the car hot or cold. After initial start it will shift normally, but does have a little of a hard time shifting when leaving stops. Most of the te when I drive very, very slow for a few blocks it will shift after starting the car. Do I need another transmission or could it be something less expensive? No dash board warning lights are on.