Think about a front focussing scope for a moment; what is the gap between say 50 and 55 yards on the front ring? Maybe 10mm between them?
Now, the AO scope works by effectively unscrewing the front element (or group) to focus on closer objects. The movement from 55 to 50 yards represents a very small increase in the length of the scope. Probably around 0.1mm.
Take that same scope and warm it up from 5 degrees to 25 degrees; the increase is 20. From O level physics we recall that the scope increases in length due to thermal expansion, and if you know the coefficient of expansion for the metal in use you can work it out. For aluminium, it's 0.000022 per degree.
If the scope is say 400mm long, then the increase in length in this example is 400mm x 20 degrees x 0.000022 which comes to 0.176mm.
So the scope has grown more in length due to temperature increase than by being refocussed from 55 to 50 yards.
Frankly it's a real surprise and an achievement that scopes shift so little with temperature.