The present invention relates to a highly energy efficient air-conditioning device (1), comprising an air/water heat pump (3), at least one extract duct (6) for discharging extract air from a building, comprising a regulator valve (33), a supply duct (9) for supplying outside air to the building, comprising a regulator valve (32), a fan (28) for forcing extract air and/or outside air over the evaporator (14) of the air/water heat pump (3), an additional heating device (12) and control means for controlling the regulator valve (32) for the supply air and the fan (28) on the basis of the flow of extract air. The present invention also relates to a method for controlling such an air-conditioning device (1).
