The domestic appliance is designed to dry a humid product by means of a process air stream that can be conducted in a process air channel, said stream flowing through a treatment chamber comprising the product and a cooling assembly for cooling and condensing the process air stream once the latter has passed through the treatment chamber. The cooling assembly has a first heat exchanger, by means of which heat from the process air stream can be supplied to a working fluid, and a heating assembly connected downstream of the cooling assembly for heating the process air stream before the latter flows through the treatment chamber, said heating assembly having a second heat exchanger, by means of which heat from the working fluid can be supplied to the process air stream. The working fluid is conducted in a heat pump, which operates according to a regenerative gas process. In the first heat exchanger, a wall temperature of a partition between a process air region and a working fluid region, at least in the vicinity of a process air inlet, lies between 50 DEG C and 80 DEG C, in particular at approximately 70 DEG C and correspondingly in the second heat exchanger, at least in the vicinity of a process air inlet, between 90 DEG C and 140 DEG C, in particular between 110 DEG C and 130 DEG C.