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Short Answer:

For all practical purposes, any metal will be both a good conductor of electricity and a good conductor of heat. Normally, the pure form of the alkali metal does conduct electricity and is also a good thermal conductor, both characteristics being a consequence of the conduction electrons in the bulk material.

Long Answer:

In this case, if we use the physics definition of metal and not the chemistry definition, then a metal is defined as a material that conducts electricity well. These electrical conductors usually have a higher thermal conductivity because the same electrons that are participating in electrical conduction are also participating in thermal conduction. In general terms then, good electrical conductors are good thermal conductors with a few notable exceptions, e.g. diamond.

Caveat:

In chemistry, a large swath of the period table labels atoms to be metals and this is not actually a proper characterization related electrical or thermal properties. These properties do not depend on the individual atoms but rather these physical properties are only manifested in bulk materials and depend on temperature, composition, crystal or amorphous structure, etc. Some materials, for instance, will change from insulating to conducting under pressure.

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