I just cooked a meat pie in the oven. Almost immediately after pulling it out of the oven, I felt that the crust was only slightly warm, but when I cut it open the filling felt very warm. I can't understand how the crust could be at a lower temperature. My understanding was that the oven heats the air, then the air heats the crust and the crust heats the filling inside. As long as the air is hotter than the crust (should be always), there is no way for the crust to lose heat, except by heating the filling and there is no way for the filling to gain heat, without being heated by the crust. According to this logic, the filling can't be hotter than the crust. Given this situation, why does the filling feel hotter than the crust?
"Feeling hotter" is a matter of heat transfer from an object to your hand. The crust of your pie doesn't transfer heat very well, whereas the somewhat liquidy innards of the pie are very good at transferring heat. It's the same reason that aluminum foil coming out of a hot oven won't burn you.