Material with low thermal conductivity are good thermal insulators (i.e. they do not absorb or transfer heat). 'Silicon Aerogel' has the lowest thermal conductivity. Other than that, materials like Polyurethane foam, Fiberglass or Foam-glass, Expanded polystyrene also have low conductivity.
Subsequently, one may also ask, why does an insulator not conduct heat through it?
An interesting fact is that poor conductors of electricity are also poor heat conductors. Wood is a much better insulator than copper. The reason is that metals that conduct electricity allow free electrons to roam through the material. This enhances the transfer of energy from one area to another in the metal.
What can conduct heat?
First, let me explain why metals generally conduct heat better than other solids do. In metals, some of the electrons (often one per atom) are not stuck to individual atoms but flow freely among the atoms. Of course, that's why metals are such good conductors of electricity.
What material is the best conductor of heat?
To my knowledge, silver is the best conductor of both heat and electricity among metals with a thermal conduction value of about 430 W/(mK). Gold and copper both come respectably close to silver, and with Copper being significantly less costly it is often chosen over silver in many applications.