Quantum memories capable of storing and retrieving coherent information for extended times at room temperature would enable a host of new technologies. Electron and nuclear spin qubits using shallow neutral donors in semiconductors have been studied extensively but are limited to low temperatures (less than or similar to 10 kelvin); however, the nuclear spins of ionized donors have the potential for high-temperature operation. We used optical methods and dynamical decoupling to realize this potential for an ensemble of phosphorous-31 donors in isotopically purified silicon-28 and observed a room-temperature coherence time of over 39 minutes. We further showed that a coherent spin superposition can be cycled from 4.2 kelvin to room temperature and back, and we report a cryogenic coherence time of 3 hours in the same system.