We need first to understand how heat spreads into a body.
When you put a heat source on a material, you are transferring energy to molecules in that point in the material. Those molecules begin to vibrate because of the energy transfer and start to collide with neighbouring molecules. In those collisions there’s a transfer of energy that propagates away from the point where the source of heat is.
In metals there are a lot of free-moving electrons that are not bond to specific atoms. Because they are not fixed in their point near an atom, they are able to do a lot of collisions with distant electrons. So they can transfer thermal energy very quickly.
In other materials (such as glass or wood) electrons are fixed in their point, and are unable to vibrate properly and to collide with other particles.
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