(I apologize for this elementary question. I don't know much about physics.)

Let's say that I put a metal pot in the refrigerator for several hours.

At this point, I guess, the pot and the air (in the refrigerator) have the same temperature.

Now, I touch this pot. It feels very cold. But when I "touch" the air (that is inside the fridge) it doesn't "feel" as cold. I don't feel the same "ouch!" that I feel when I touch the pot.

Why is that? Why does the metal seem colder than air although they both have the same temperature?

(I know that gas has less particles in it in one unit of volume compared to solids and liquids, but since "temperature" means "the average kinetic energy", these fewer air particles are supposed to hit my hand in a velocity that's going to compensate for their lower number, aren't they?)

A related question, for clarification:

If I use a thermometer to measure the temperature of the pot & air (let's assume it's a thermometer that has a probe that can touch objects), will it show the same reading for both? If so, what makes the thermometer different than my hand? I mean, my hand is sort of a thermometer, so why would it fail whereas a non-human thermometer would work?