B777 ferry flight returns to departure airport after experiencing an apparently false fire warning in the crew rest area during the climb.

Narrative

On climbout we had a Master Warning light and bell. The EICAS had a message for smoke FDCR (flight deck crew rest). The Captain; who was the Pilot Flying; also took over ATC and I started the checklist. I had to get out of my seat since we were flying a ferry flight. There were only the two of us on the aircraft; so I had to evaluate the FDCR and see if there was smoke or fire. I took a PEB; checked the cockpit door for heat; there was none; looked out the peep-hole -- saw nothing; then opened the door looking for any signs of smoke or fire. I checked the FDCR and found the heater on but no smoke or fire. I did notice a particular odor. The Captain was continuing to run the checklist and I re-set the FA panel to silence the warning bell. I returned to the cockpit; closed and secured the door; and finished the required checklist. The Captain coordinated for a return to ZZZ and we landed on Runway 18R. We were met by ARFF which came aboard and searched for any hot spots. The firemen spent over 1 hour looking for the source of the warning. We turned the aircraft over to Maintenance.