Congratulations. Your friends think highly enough of you to put out their company tableware, which is made of sterling silver. Your home “silverware” is either stainless steel or (sorry about that) only silver-plated base metal.
Sterling silver is almost pure silver: 92.5 percent, to be exact. And silver is the best conductor of heat among all the metals.
Heat will always move from a place of higher temperature to a place of lower temperature if it can find any way to get there, and silver provides a superb heat highway. All the spoon did was to conduct the coffee’s heat out of the cup and into the cooler room or, when you touched it, into your fingers.
During the process of being a conduit for all that heat, the spoon itself becomes hot, approximately the same temperature as the coffee, even though you might think it’s hotter. (I don’t recommend sticking your finger into the coffee to prove that.)
Stainless steel conducts heat less than one-fifth as fast as silver does. At home you probably never leave your everyday spoon in the coffee long enough for it to get very hot at the handle end. Even if you did, it wouldn’t conduct its acquired heat into your fingers fast enough to be uncomfortable.