I was thinking something like this too.
Does the stick stop as soon as the engine is off? Or does it need to cool some? Only things I can come up with would be something with vacuum though I don't see how, unless the throttle does not control the flaps like it does on my v45.
If it sticks for a bit, I could see heat causing something to bind then, most likely the rod the flaps bolt to.
The ride IS the adventure. The destination is just to get gas!