A wearable breathing apparatus includes a thermal capacitor that a user inhales and exhales through. Inhaled air is cooled as it passes through the thermal capacitor, and exhaled air cools the material of the thermal capacitor for the next breathing cycle. The breathing apparatus may be used by a firefighter, for example, as a lightweight apparatus to enable the firefighter to safely breathe dangerously heated air, for example while in a fire shelter, that may otherwise cause injury to the user. The breathing apparatus advantageously does not require external power for cooling. The thermal capacitor may also be used as a part of a rebreather that uses a scrubber that removes carbon dioxide from exhaled air, for rebreathing. Further, the thermal capacitor may be used for other purposes, such as in recirculation of building air.