Like nothing. Mirrors work with light. If no light is present, they don't reflect anything. Also, if nothing was in the room, does that include people? Because you can't know what something is like in a room with nobody there to observe it.
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From my understanding of thermal energy and photons, the photons have to be emitted on something that can conduct a significant amount of heat and has free electrons. Sure the mirror will convert some of the photons to heat, but the action of reflecting photons won't make thermal energy.