What type of compounds conduct heat?

For conduction of heat (or electricity), free carrier electrons are required. Generally, ionic compounds are better conductors of heat (and electricity) when in molten form or when dissolved in the water. In comparison, covalent compounds are generally bad conductors of heat (graphite is an exception). In the case of ionic compounds, in the molten state or when dissolved in water, free carriers (electrons) are available for conducting heat. In case of covalent compounds, the electrons are exchanged between the constituents, and hence, free electrons are not available for conducting heat (or electricity). Thus, the lack of free carriers causes covalent compounds to be (generally) insulators—the opposite of conductors. Ionic compounds such as sodium chloride (NaCl), on the other hand, readily dissolve in water and form ions (sodium and chloride, in this case) that can allow the solution to conduct heat (and electricity).
Metals are also good conductors of heat due to the availability of electrons that can vibrate and also move around. When one end of a metal is heated, the electrons in the hot region gain more kinetic energy and bump into the neighboring electrons, thus transferring the kinetic energy. This ensures that heat is conducted from the hot end to the colder end of the metal. Metals such as copper, silver, and aluminum are good conductors of heat.
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