Radiative cooling has recently garnered a great deal of attention for its potential as an alternative method for photovoltaic thermal management. Here, we will consider the limits of radiative cooling for thermal management of electronics broadly, as well as a specific application to thermal power generation. We show that radiative cooling power can increase rapidly with temperature, and is particularly beneficial in systems lacking standard convective cooling. This finding indicates that systems previously operating at elevated temperatures (e.g., 80°C) can be passively cooled close to ambient under appropriate conditions with a reasonable cooling area. To examine these general principles for a previously unexplored application, we consider the problem of thermophotovoltaic (TPV) conversion of heat to electricity via thermal radiation illuminating a photovoltaic diode. Since TPV systems generally operate in vacuum, convective cooling is sharply limited, but radiative cooling can be implemented with proper choice of materials and structures. In this work, realistic simulations of system performance are performed using the rigorous coupled wave analysis (RCWA) techniques to capture thermal emitter radiation, PV diode absorption, and radiative cooling. We subsequently optimize the structural geometry within realistic design constraints to find the best configurations to minimize operating temperature. It is found that low-iron soda-lime glass can potentially cool the PV diode by a substantial amount, even to below ambient temperatures. The cooling effect can be further improved by adding 2D-periodic photonic crystal structures. We find that the improvement of efficiency can be as much as an 18% relative increase, relative to the non-radiatively cooled baseline, as well as a potentially significant improvement in PV diode lifetime.