(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?

Short answer:

The thermometer measures actual temperature (which is the same for both), while your hand measures the transfer of energy (heat), which is higher for the pot than the air.

Long answer: 

Keyword: Thermal Conductivity

The difference is a material-specific parameter called thermal conductivity. If you are in contact with some material (gas, liquid, solid), heat, which is a form of energy, will flow from the medium with higher temperature to the one with low temperature. The rate at which this happens is determined by a parameter called thermal conductivity. Metals are typically good heat conductors, which is why metal appears colder than air, even though the temperature is the same.  

Regarding your second question: the thermometer will show the same temperature. The only difference is the time at which thermal equilibrium is achieved, i.e. when the thermometer shows the correct temperature.

Final remark: the rate at which heat (energy) is drained from your body determines whether you perceive a material as cold or not, even if the temperature is the same. 

For reference, here is a table which lists thermal conductivities for several materials: 

  
