Fermi energy is the average energy possessed by electrons participating in conduction in metals at T>0K?

Question

I don't understand why on pg 963 of the following book stating that Fermi energy is the average energy possessed by electrons participating in conduction in metals at T>0K. Should Fermi energy be higher? And unlike Fermi energy level, the average energy possessed by electrons participating in conduction should increase as temperature increases according to Fermi-Dirac distribution curve so I don't get how they can be the same?

NOTE: Scrolling up and down multiple times after you enter the page you can see pg 961-965. https://books.google.ca/books?id=sDscEAAAQBAJ&pg=PA963&lpg=PA963&dq=fermi+energy+is+the+average+energy+possessed+by+electrons+participating+in+conduction+in+metals+at+temperatures+above+0k&source=bl&ots=t0WO-_-x5Y&sig=ACfU3U3JL57aLDbwKoguStMc-iIk-vdPcw&hl=en&sa=X&ved=2ahUKEwiTm7z_zZ36AhW0Jn0KHQXnDc8Q6AF6BAgwEAM#v=onepage&q=fermi%20energy%20is%20the%20average%20energy%20possessed%20by%20electrons%20participating%20in%20conduction%20in%20metals%20at%20temperatures%20above%200k&f=false

Answer 1

The definition is incorrectly stated. Electrons below the Fermi energy do not participate in conduction. One operational definition of the Fermi energy in metals is that it is topmost energy in the valence band at absolute zero temperature. The average energy for electrons that participate in conduction is found by integrating energy over all electrons above the Fermi energy. You are correct, this value increases as temperature increases.