Verified answer

When two objects of different temperature come into contact, they exchange energy (from hot to cold) until they are both at the same temperature.

How much energy they exchange depends on a quantity called the "specific heat" of a material...that is, objects with higher specific heats store more energy than objects with lower specific heats (at the same temperature).

The specific heat of water (which is most of your coffee) is about 3 times that of silver. So, when the water touches your tongue, it gives up more energy and is more likely to result in a burn.

Metal can change its temperature fairly quickly to adjust to your tongue, but coffee won't. So its mostly about what is made of. Still is you have hot enough coffee and the spoon has been there for quite a while you can still burn yourself

Mostly due to specific heat.

Compare the specific heat of water to that of silver in a table like this one:

http://hyperphysics.phy-astr.gsu.edu/hbase/tables/...

The number for water is 18 times higher than the number for silver. That means that for every degree that a gram of water cools, it releases 18 times as much heat energy as a gram of silver cooling by one degree.