In this Straight Dope Classic, Cecil states that metal feels colder than wood because of its higher thermal conductivity, which pulls heat out of your hand faster.
But conductivity itself is not the sole determinant - the important quantity is actually the thermal effusivity (square root of [conductivity times heat capacity]) of the two materials relative to the thermal effusivity of the human hand. Depending on the heat capacities, the colder-feeling material could have either higher or lower thermal conductivity compared to the hotter-feeling material. More here.
This reminds me of another thing I’ve thought about: How do we know things are wet? If you sit in a puddle of water or touch something wet you know it instantly. Does our skin have water sensors? No - again, it’s temperature we’re feeling. Water usually increases the heat conductivity of the surface and makes it feel colder than it would otherwise.
Ever been wearing thin gloves (examination type) to protect your hands when cleaning? Get something oily on them, and it will feel “wet” to your hands, even though your skin is perfectly dry. Kind of creepy. I thought I had punctured the glove and my hand was getting wet, but when I pulled the glove off, the sensation left instantly.
Whether something feels hot to you or not also depends on the mass of the hot object. Put you hand on a very hot piece of foil and it will not feel hot. A piece of 1in. thick steel at the same temperature will burn you badly instantly.
I think that’s because the thin sheet of foil has very little heat stored up due to the small amount of mass. It can’t hold as much of any temperature. I am guessing that aluminum foil and thick steel have different rates of transferring that temperature.
Yes, that is heat capacity. It also probably goes to thermal effusivity (as stated above for cold things). But if both plates are the same material (i.e. aluminum), then the differing factor is heat capacity.