We derive a fluctuation–dissipation theorem describing thermal electromagnetic fluctuation effects in nonlinear media that we exploit in conjunction with a stochastic Langevin framework to study thermal radiation from Kerr photonic cavities coupled to external environments at and out of equilibrium. We find that in addition to thermal broadening due to two-photon absorption, the emissivity of such cavities can exhibit asymmetric, non-Lorentzian lineshapes due to self-phase modulation. When the temperature of the cavity is larger than that of the external bath, we find that the heat transfer into the bath exceeds the radiation from a corresponding linear black body.We predict that these temperature-tunable thermal processes can be observed in realistic cavities at or near room temperature.