We describe a low-temperature thermodynamic model for dynamic nuclear polarization (DNP) via continuous-wave partial saturation of electron spin resonance (ESR) lines that are both homogeneously and inhomogeneously broadened. It is a variant of a reasoning proposed by Borghini, which in turn used Redfield's thermodynamic treatment of saturation. Our variant is furthermore based on Provotorov's insight that under partial saturation of a coupled-spin system two distinct spin temperatures should appear in a thermodynamical theory. We apply our model to DNP results obtained at a temperature of 1.2 K and in magnetic fields of 3.35 and 5 T on 1-C-13 labeled sodium acetate dissolved in a frozen D2O/ethanol-d(6) solution doped with the free radical TEMPO.