A spinning wheel is brought into contact with an identical wheel...

As the wheel slows down due to friction, its angular velocity decreases. Therefore, its kinetic energy decreases.

Mechanical energy is the sum of kinetic and potential energy. Since the potential energy remains constant and the kinetic energy decreases, the mechanical energy also decreases.

The work done by friction generates heat, which raises the temperature of the wheels. This causes an increase in the internal energy of the wheels.

By symmetry, the heat generated is shared equally between the two identical wheels. The decrease in the mechanical energy of the first wheel is exactly compensated by the increase in its internal energy. Thus, the total energy of the first wheel remains constant.

Hence, only the mechanical and kinetic energies of the first wheel decrease.