I hadn't heard of the term "Fermi velocity", but if it is the classical velocity derived from the Fermi energy, that should only be a lower bound on the average

I hadn't heard of the term "Fermi velocity", but if it is the classical velocity derived from the Fermi energy, that should only be a lower bound on the average speed of the electrons in the metal. That said, I don't remember the orders of magnitude here, the relevant question being how cold "room temperature" is with respect to the Fermi level -- a quick Google suggests quite cold, in which case the Fermi velocity should be a very good approximation. In which case, it's interesting to realise that the motion of the electron gas comes mainly from Pauli exclusion rather than thermal noise! It's not a result I would have expected.