Due to the wires having electrical opposition, which means that they resist the movement of electrons, the electrons bump into atoms on the outside of the wire, and their kinetic energy is given to the atoms as thermal energy. This thermal energy causes the wires to heat up.
A higher current for a given voltage means a lower resistance. The thicker wire has a lower resistance than the thinner wire. The resistance of a wire decreases with increasing thickness. Current through a wire causes power loss from the wire resistance. They resist the motion of the electrons.