# Temperature, Kinetic Energy, and Chemical Potential

I have a confusion that in an Homogeneous electron gas.

When $T=0$, we know that $\mu=E_F$.

So Kinetic Energy per electron=$\frac{3}{5}E_F=\frac{3}{5}\mu$.

I thought that Temperature is related to kinetic energy. How can $T=0$ condition can have kinetic energy?