Can Fermi energy be estimated experimentally?

Fermions, particles with half integral spin, follow Fermi-Dirac distribution. For free electron gas at absolute zero, Fermi energy is the energy of highest occuped level by electron. For n, which is density of free electrons, Fermi energy can be estimated by E_F= h² (3π²n)^2/3/(8mπ²) [1]. Theoretical calculation of Fermi energy of a metal involves estimation of density of electrons utilizing number of valence electrons. Experimentally, Fermi energy can be estimated by measurement of density of electrons in Hall effect measurement at room temperature. The measurement at room temperature serves as a good approximation because of very less difference between electron distribution at 0K and 300K.
[1] Modern Physics, K. Krane Wiley
Unscientific determination of Fermi energy by heating and/or cooling a copper wire, C. Kotabage, A. C. Abhyankar, Resonance- Journal of Science Education, 24 (12), 1439-1443.