How would a metal spoon help to make cup of hot tea cool down?

A metal spoon actually increases the *rate* at which a cup of hot tea cools down.

A metal spoon is a good *conductor* of heat. This means that when you put a metal spoon in a cup of hot tea, the heat from the tea transfers to the spoon. The spoon then dissipates the heat into the surrounding air. This causes the tea to cool down more quickly.