Accurate models of radiative cooling are a fundamental ingredient of modern cosmological simulations. Without cooling, accreted baryons will not efficiently dissipate their energy and collapse to the centres of haloes to form stars. It is well established that local variations in the amplitude and shape of the spectral energy distribution of the radiation field can drastically alter the cooling rate. Here we introduce deepCool, deepHeat, and deepMetal: methods for accurately modelling the total cooling rates, total heating rates, and metal-line only cooling rates of irradiated gas using artificial neural networks. We train our algorithm on a high-resolution cosmological radiation hydrodynamics simulation and demonstrate that we can predict the cooling rate, as measured with the photoionisation code CLOUDY, under the influence of a local radiation field, to an accuracy of ~5%. Our method is computationally and memory efficient, making it suitable for deployment in state-of-the-art radiation hydrodynamics simulations. We show that the circumgalactic medium and diffuse gas surrounding the central regions of a galaxy are most affected by the interplay of radiation and gas, and that standard cooling functions that ignore the local radiation field can incorrectly predict the cooling rate by more than an order of magnitude, indicating that the baryon cycle in galaxies is affected by the influence of a local radiation field on the cooling rate.