Sorry, this is not an easy question to answer. Unfortunately, there can be several causes for this symptom. It could be due to hardened internal rubber lip seals on servos or clutch drum piston, sticking valves or an electronic computer system problem on a newer vehicle.
When the transmission is cold, the lip seals can stick in their “at rest” positions. When fluid pressure is first applied, they will not move for a while, but when they finally do, they will function until the transmission cools down and the process is repeated. When the transmission reaches operating temperature, the seals are often softened enough to function properly. Invariably, this problem will get worse with age and colder temperatures.
Additives that are formulated to soften internal seals will usually do more harm than good for the transmission in the long run. There is no way to control the affect that additives have on seals, and therefore, the repair of the problem to is overhaul the transmission. The degree of “hardness” of the various seals in a transmission will vary greatly. The seals that are not hard will be softened to a gummy, swollen mush.
If the cause is sticking valves, you may have worn parts in the transmission depositing metallic debris in the transmission pan. This debris then gets sucked into the valve body and the valves stick. The sticking valves can delay shifts and cause other strange problems.
Pressure tests, a pan inspection or other tests are usually necessary to find the actual cause of the symptom. If parts are wearing inside of the transmission, it will need to be taken apart to find worn parts and replace them. If the transmission has very many miles on it, or very much debris in it, that usually means an overhaul.
If your transmission is electronically controlled, the problem may also be due to a problem with a sensor, the computer system, wiring, connectors, solenoids, etc. Again, diagnostic tests would be necessary to pinpoint the cause of the problem and correct it. The good news is that you may not need an overhaul in this case. The bad news is that sometimes the cause of the problem can be difficult to pinpoint. Therefore the number of tests and the charges may be higher.