We propose a mechanism design based approach for the temperature setting in shared spaces (such as meeting rooms, library, and open office areas) in buildings. The proposed mechanism asks each occupant to report her willingness-to-pay for three possible outcomes: keeping the current temperature, lowering the temperature for one degree, and raising the temperature for one degree. Collecting the occupants' preferences, the proposed mechanism chooses the outcome that maximizes the social welfare, i.e., the sum of all occupants' willingness-to-pay (the overall thermal comfort of all occupants) minus the energy cost. The (normalized) energy cost is shared among occupants in a fair manner, according to a generalized Arrow-d'Aspremont-Gerard-Varet (AGV) mechanism. The proposed generalized AGV mechanism ensures that all occupants obtain the same (ex-ante) net payoff, while maintaining Bayesian incentive compatibility, ex-post efficiency, and ex-post budget balance of the standard AGV mechanism. We implement the proposed mechanism in an experiment with 30 students. Numerical results (based on the true temperature preferences reported by participating students) demonstrate that the proposed mechanism can lead to Pareto-better performance (in terms of energy cost and thermal comfort) than existing approaches, and fairer payment distributions than the standard AGV mechanism.