The specific heat capacity is the amount of work (Joules) required to raise a unit temperature of a unit volume of material. Thermal conductivity on the other hand is the heat flux (delta t) measured when an amount of unit heat is passing a unit distance through material a unit area thick. Specific heat capacity will not matter in a waterblock with a state of equilibrium i.e. the final temperature has been reached. Zinc is worse than aluminium at conducting heat.
Hope I didn't make a mistake.
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