An air conditioning arrangement for an aircraft with a plurality of climate zones that may be individually temperature-controlled includes a main branching system having an air supply feed path system with a mixing chamber and a plurality of sub-branching systems branching from the mixing chamber and leading to one of the climate zones in each case. Basic temperature control means are used for controlling the temperature of the air supply in the mixing chamber. Individual temperature-control means are used on the other hand for individually controlling the temperature of the air supply in each of the sub-branching systems as a function of a desired temperature value of the respective climate zone. Basic temperature control of the air supply in the mixing chamber preferably takes place independently of a temperature requirement of the climate zone with associated combined heat and power engine.