Radiative transfer modeling is a complex and computationally expensive process that is used to predict how radiation interacts with the atmosphere and Earth's surface. The Rapid Radiation Transfer Model (RRTM) is one such process model that is used in many Earth system models. In recent years, there has been a growing interest in using machine learning (ML) to speed up radiative transfer modeling. ML algorithms can be trained on large datasets of existing RRTM simulations to learn how to predict the results of new simulations without having to run the full RRTM model so one can use the algorithm for new simulations with very light computational demand. This study developed a new physics-based ML emulator for RRTM that is built on a convolutional neural network (CNN) where we trained the CNN on a dataset of 28 years of RRTM simulations. We built a custom loss function, which incorporates information on how radiation interacts with clouds at day- and night-time. The emulator was able to learn how to predict the vertical heating rates in the atmosphere with a high degree of accuracy (RMSE of less than 2% and Pearson's correlation above 0.9). The new ML emulator is over 56 times faster than the original RRTM model on traditional multi-CPU machines. This speedup could allow scientists to call the RRTM much more frequently in atmosphere models, which may improve the accuracy of climate models and reduce the uncertainty in the future climate projections.