We report the first 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 proportional to 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, a direct consequence of Pauli blocking. In a unitary Fermi gas, we observe that the JT heating is marginal in the temperature range 0.2 less than or similar to T=T F less than or similar to 0.8 as the repulsive quantum-statistical effect is lessened by the attractive interparticle interactions.