OK, I just know sometimes the car can put pressure on the parking pawl.
For further clarification, the whole box is hydraulically controlled. As soon as the engine is running, the pump is running. It provides pressure to the hydraulic valves and clutches, with the solenoids switching pressure to the various valves, to control the hydraulic clutches and change gear when needed. All of this also, as a by product will get fluid going everywhere. Now I wonder if your box is a little low on fluid? It could also be unrelated to the box itself, as the selector and cable sit above the exhaust. It could be heat from the exhaust freeing something up.