Digital cameras are used in a large variety of scientific and industrial applications. For most applications, the acquired data should represent the real light intensity per pixel as accurately as possible. However, digital cameras are subject to physical, electronic and optical effects that lead to errors and noise in the raw image. Temperature- dependent dark current, read noise, optical vignetting or different sensitivities of individual pixels are examples of such effects. The purpose of radiometric calibration is to improve the quality of the resulting images by reducing the influence of the various types of errors on the measured data and thus improving the quality of the overall application. In this context, we present a specialized neural network architecture for radiometric calibration of digital cameras. Neural networks are used to learn a temperature- and exposure-dependent mapping from observed gray-scale values to true light intensities for each pixel. In contrast to classical at-fielding, neural networks have the potential to model nonlinear mappings which allows for accurately capturing the temperature dependence of the dark current and for modeling cameras with nonlinear sensitivities. Both scenarios are highly relevant in industrial applications. The experimental comparison of our network approach to classical at-fielding shows a consistently higher reconstruction quality, also for linear cameras. In addition, the calibration is faster than previous machine learning approaches based on Gaussian processes.