P Wells of Levin asks :-
Why does the handle of a cup not get hot when the cup is?
Geoff Barnes, a physicist at Massey University, responded.
Cups are usually made of materials that are not very good conductors of heat. Many cups are made of plastic, glass or porcelain materials that typically conduct heat more than 100 times worse than stainless steel. Note, however that porcelain conducts heat ten times better than wood. (Tiles feel colder to stand on than a wooden floor at the same temperature).
The handle is likely to remain cooler than the hot vessel because of heat losses from the handle, and the temperature drop associated with heat conduction. The handle has a relatively large surface area to volume ratio, (small cross-sectional area) and so convective and radiative heat losses are likely to play their part.
As you hold the cup, your fingers will also conduct heat away, and so help keep the handle cooler.
Heat energy is naturally conducted from the hotter parts to the cooler parts of an object. The greater the length of the conductive path between the hotter and cooler parts, the longer the cooler parts will stay cool. Thus the parts of the handle furthest from the hot container will stay cooler longer.
Thermal (heat) conduction is associated with the rapid vibrations of the atoms of the hot regions of a material. These energetic atoms vibrate against adjacent atoms, which can absorb energy from the interactions, and hence get warmer.