Energy can be conducted through matter. The rate
of energy transfer is proportional to the thermal gradient (the
change in temperature per length unit)
and the area of the conducting medium and a materials parameter
called the thermal conductivity:
Thermal conduction can take place through propagating vibrations: sound waves
and through electronic transport in metals. The thermal conductivity of
materials varies by many orders of magnitude. When we want to thermally isolate
we use thick and poor thermal conductors such as Styrofoam or some other
very lightly packed material. When we want good thermal conduction
for example between a hot plate and our food we use a thin metallic plate.
We have a demonstration experiment showing how different materials
have different abilities to conduct heat.