A heat exchanger has a plurality of fluidically parallel first layers which define first heat exchanger ducts through which a first medium is capable of flowing, and in each case has a second layer between the two first layers. The respective second layer is in thermal contact with the two adjacent first layers and defines at least one second heat exchanger duct through which a second medium is capable of flowing in parallel. The respective second layer comprises two fluidically parallel layer plies. A controllable supply of the second medium to the one and/or the other layer ply in each case is provided. Such a heat exchanger can be used, in particular, as an evaporator with an integrated starting and main evaporator part, and particularly as an evaporator in a reforming plant of a fuel-cell vehicle.