Statistical mechanics demands that the temperature of a system is positive provided that its internal energy has no upper bound. Yet if this condition is not met, it is possible to attain negative temperatures for which higher-order energy states are thermodynamically favored. Although negative temperatures have been reported in spin and Bose-Hubbard settings as well as in quantum fluids, the observation of thermodynamic processes in this regime has thus far remained elusive. Here, we demonstrate isentropic expansion-compression and Joule expansion for negative optical temperatures, enabled by purely nonlinear photon-photon interactions in a thermodynamic microcanonical photonic system. Our photonic approach provides a platform for exploring new all-optical thermal engines and could have ramifications in other bosonic systems beyond optics, such as cold atoms and optomechanics.