Does spin degeneracy affect ideal Fermi gases in any way as T->Infinity? In other words, given any system comprised of an ideal Fermi gas, in the high-temperature (classical) limit, are there any observable thermodynamic quantities (pressure, volume, energy, density, etc.) that change if you change nothing else about the system other than the spin degeneracy of the particles?
 A: I would say that the question is still not very well defined, as it is important if in the high-temperature (classical) limit spin is conserved or not.
If spin is conserved (think strong magnetic fields $B\gg T$), then in the classical limit spinful quantum gases become a mixture of classical gases, as coherent superpositions between spin states are not allowed (thus no x or y components of magnetization). In the case of spin-1/2, we end up with a binary mixture (up and down) of classical particles with different chemical potentials (due to the magnetic field). Obviously, this mixture behaves very differently from a single species of particles.
On the other hand, if spin is not conserved, temperature can induce spin flips, and in the high temperature limit  ($B\ll T$) there is no difference between up and down. In this case, the only difference as compared to the behavior of a single species of classical particles is a different density of states. In other words, there are twice as many states to occupy. I am hesitant to say that nothing changes (for example, the relation between the chemical potential and the particle density changes), however, my guess would be that such physically measurable thermodynamic quantities as pressure and entropy are unaffected by spin.
