No metals do not cool off quickly.
Runners do not sit on metal chairs after a race because their muscles are warm and metal can cool them off too quickly causing cramps.
Heat the metal red hot. To harden the metal, cool it quickly by dunking it into cold water. To get a soft metal, let it cool slowly.
Tea in a metal cup would cool down relatively quickly, since the metal cup wall conducts heat very well.
The only explanation of tempering is in metal manufacturing. Heat metal to cherry hot, plunge metal into water to quickly cool metal, hardened metal is created
separate the pieces and put them on an unheated metal tray
It will cool quicker with the lid off, but aside from that it makes no difference. (Although for food hygiene purposes it is better to cool it off quickly and then put it in the fridge).
Yes it would, the metal conducts the heat quickly
Because metal is a good conductor of heat it absorbs heat from material touching its surfaces, and transfer to air.
water in a metal mug cools down quicker because the air around the mug cools the metal therefor cooling the water inside the mug
Yes the Obsidian does cool quickly and the vesicular basalt
A desert will cool off much more quickly as there is little humidity or cloud cover that would hold in the heat of the day.
Basalt cools off quickly because it is formed under water.