When a metal is heated, the free electrons gain
a. elastic energy
b. potential energy
c. kinetic energy
d. nuclear energy

Explanation:

Heat is energy in transit, in fact it is a transfer of thermal energy from one body to another.  

So, when a metal is heated is because we have two bodies with different temperatures and thermal energy is transferred from one body to another, implying a high speed and kinetic energy in the particles involved (electrons in this case).

This is because the kinetic energy of a particle is that energy it possesses due to its movement, and according to the first principle of thermodynamics, there is a relationship between heat and movement, since the metal is composed of particles that are in motion (to a certain extent).

In this way, with the increase of the temperature of the metal, there is an increase of the kinetic energy of its free electrons with a gain of velocity (movement), therefore a gain in kinetic energy.