Intense thunderstorms threaten life and property, impact aviation, and are a challenging forecast problem, particularly without precipitation-sensing radar data. Trained forecasters often look for features in geostationary satellite images such as rapid cloud growth, strong and persistent overshooting tops, U- or V-shaped patterns in storm-top temperature (and associated above-anvil cirrus plumes), thermal couplets, intricate texturing in cloud albedo (e.g., “bubbling” cloud tops), cloud-top divergence, spatial and temporal trends in lightning, and other nuances to identify intense thunderstorms. In this paper, a machine-learning algorithm was employed to automatically learn and extract salient features and patterns in geostationary satellite data for the prediction of intense convection. Namely, a convolutional neural network (CNN) was trained on 0.64-μm reflectance and 10.35-μm brightness temperature from the Advanced Baseline Imager (ABI) and flash-extent density (FED) from the Geostationary Lightning Mapper (GLM) aboard GOES-16. Using a training dataset consisting of over 220,000 human-labeled satellite images, the CNN learned pertinent features that are known to be associated with intense convection and skillfully discriminated between intense and ordinary convection. The CNN also learned a more nuanced feature associated with intense convection—strong infrared brightness temperature gradients near cloud edges in the vicinity of the main updraft. A successive-permutation test ranked the most important predictors as: 1) ABI 10.35-μm brightness temperature, 2) ABI GLM flash-extent density, and 3) ABI 0.64-μm reflectance. The CNN model can provide forecasters with quantitative information that often foreshadows the occurrence of severe weather, day or night, over the full range of instrument-scan modes.