1) When you burn yourself, heat has to flow from the pie or the pie plate into your finger. Dont do this, but if you were to hold your finger to the "fresh cooked" pie for a few seconds, you would notice that you do start to become uncomfortable - the pie can still burn you (to an exent) but not as quickly. This is because the pie has a much lower "thermal conductivity" than the metal - heat can flow from the pie plate to your hand much faster than from the pie - despite the pie and the pie plate being the same temperature.
2) if you keep your hand in contact with either the pie or the plate, after some time, your hand and the object you're touching willreach the same temperature. At this point, the flow of heat will stop. Compared to the pie material, metal also has a very high "heat capacity" - that means it holds a lot more heat energy per degree of temperature than the pie. So, not only does the heat flow quickly from the metal, the metal also stays hot - the equilibrium temperature will be higher than the pie (unless the pie is huge and the plate is tiny) - so the flow of heat is faster and results in a higher final temperature. On the otherhand, as the pie loses energy into your hand it raising the temperature of your hand to an intermediate value, so you only absorb a smaller, less damaging amount of heat and it happens over a slower time, so much of the potentially damaging heat energy can escape intot he rest of your body - spread out of your whole body (or even your whole arm) the heat is much less intense.