Abstract: We present the first thermodynamically correct calculation of the noise in a simple nonlinear resistive bolometer or calorimeter operated out of equilibrium. The solution is rigorous only for first- and second-order deviations from equilibrium, and for the linear and quadratic terms of dissipative elements. In contrast, existing models of noise in resistive bolometers are based on the application of equilibrium theories to a system that is often nonlinear and out of equilibrium. We derive solutions applicable both in and out of steady state. The noise has power spectral density different from the equilibrium theory, and it has higher-order correlations and non-Gaussian characteristics. The results do not apply to non-Markovian hidden variables in the bolometer.