Indeed, at least at this level (get onto particle physics / astrophysics / quantum mechanics etc. and "opinions will vary"
). Traditional physics was not a matter of opinion when I was at uni, and still isn't
[mind you (our understanding of) even 'traditional physics' is not set in stone, as the likes of Einstein have demonstrated - and, of course, Physics once 'said' that everything orbited around planet Earth! ]! Anyway ....
I would say not "at least" for all parts of the pan - that will only be true for the parts of the pan through which heat is travelling
into the pan - and, in fact, since metal is a very good conductor, even for the base, the outside temp will not be much above the ~100°C temp of the inside surface of the base . For other parts of the pan (i.e. the 'sides'), where heat is travelling
out of the pan into the surrounding air (IF you accept that happens - see below), the temp gradient is in the opposite direction, so the outside of the pan will be (again, probably only fractionally, due to the good conductance of metal) below (not 'at least") the ~100°C temp of the inside surface of the sides.
Ah - are you saying that you don't believe that heat from within the pan will 'lost' from the sides of the pan into the surrounding air?
Whatever, quite part from theory, we have the empirical evidence from my experiment this afternoon to consider. I was able to touch, for a few seconds, the outside of a kettle in which water was being boiled - and I think I would now 'have the scars' had that been "...surely more than 100⁰C" ?
Once all the water (which was the only thing 'capping' inside-pan temps at ~100°C) has gone, the goalposts will obviously have totally moved, and all of the pan will try to rise to a temp approaching that of the source (flame or whatever), failing to completely achieve that goal only because of heat loss into the surrounding air etc..
Kind Regards, John