A good electrical conductor is a material that has a lot of free charges that can easily move across the material, and with a large mean free path.
Now let's assume that one side of the material is at higher temperature than the other side. The charges on the hotter side move faster than the charges on the cooler side, so the faster charges transfer part of their energy to the charges of the cooler side by collisions. The larger the number of free charges (and the larger their mean free path), the faster is this transmission of energy (which is basically transmission of heat), so the larger is the thermal conductivity of the material, so a good electrical conductor is generally also a good thermal conductor.
