  We report the observation of the quantum Joule-Thomson (JT) effect in ideal
and unitary Fermi gases. We study the temperature dynamics of these systems
while they undergo an energy-per-particle conserving rarefaction. For
scale-invariant systems, whose equations of state satisfy the relation
$U\propto PV$, this rarefaction conserves the specific enthalpy, which makes it
thermodynamically equivalent to a JT throttling process. We observe JT heating
in an ideal Fermi gas, stronger at higher quantum degeneracy, a result of the
repulsive quantum-statistical `force' arising from Pauli blocking. In a unitary
Fermi gas, we observe that the JT heating is marginal in the temperature range
$0.2 \lesssim T/T_{\mathrm{F}} \lesssim 0.8 $ as the repulsive
quantum-statistical effect is lessened by the attractive interparticle
interaction.
