The present invention relates to a blood treatment device having a heat exchanger which has a first space and a second space, wherein the first space is flowed through by a first fluid and the second space is flowed through by a second fluid, and wherein the heat exchanger has a membrane which separates the first space from the second space, wherein the membrane forms a component of a capacitor which has two capacitor plates between which the membrane is located, and wherein monitoring means are provided which are connected to the capacitor and which are configured such that they detect an electrical property of the capacitor for the purpose of detecting a leak from the first space to the second space.