Thermal monitoring is important not only to ensure the comfort of building inhabitants but also to reduce energy consumption and greenhouse gas emissions. It can be, however, a challenging task because of limited computational and sensing resources at hand. This paper provides an efficient technique to estimate average (or mean operative) temperatures of rooms in a building. The proposed average observer is of minimum order whose parameters are chosen to minimize the asymptotic estimation error. The results show the effectiveness of the approach in the estimation-based temperature regulation.