You'll need to decide what you mean by "stopped moving" - how long does the mouse have to remain motionless to qualify? And is just being within the hot zone sufficient, or must the mouse be completely motionless within that area?
Anyway, one approach would be to use a QTimer set to your timeout interval, and reset the timer with each mouse move. If the timer ever times out, it'll emit a signal which you can connect to your popup dialog.
Personally, I think it would be better - and simpler - to just pop up the dialog when the mouse is within the hot zone, and ignore timing and whether the mouse has "stopped." But this is a rough guide if you decide to proceed.
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