The heat capacity of a material is a fundamental property that is of significant practical importance. For example, in a carbon capture process, the heat required to regenerate a solid sorbent is directly related to the heat capacity of the material. However, for most materials suitable for carbon capture applications the heat capacity is not known, and thus the standard procedure is to assume the same value for all materials. In this work, we developed a machine-learning approach to accurately predict the heat capacity of these materials, i.e., zeolites, metal-organic frameworks, and covalent-organic frameworks. The accuracy of our prediction is confirmed with novel experimental data. Finally, for a temperature swing adsorption process that captures carbon from the flue gas of a coal-fired power plant, we show that for some materials the energy requirement is reduced by as much as a factor of two using the correct heat capacity.