Local tissue areas should be thermally destroyed when using ultrasound thermotherapy. Traditionally, mono-frequency continuous wave ultrasound signals are used to this end. These lead to a non-optimal distribution of heat or to a non-optimal localization of the heating inside the tissue. In practice, the following dosage problem arises: the prevention of unwanted tissue damage in the tissue located in front of the target area while simultaneously having a sufficiently high damaging effect in the target area. The aim of the invention is to optimize the distribution of heat or to increase the localization of the heating. To these ends, modified transmitted signals (e.g. multi-frequency signals) are used that are adapted to a specific utilization of the non-linear ultrasound propagation and attenuation properties inside the tissue. This enables, while limited to the target area, a non-linear heating yield caused by non-linear ultrasound effects to be achieved that drastically improves the localization of the heating. Due to this optimization, the problem of dosage is substantially eased, and it is possible to thermally destroy even deep-lying tumors without unwanted burning of the tissue located in front of the tumors. This results in both improving the practical usability of ultrasound thermotherapy and in further reducing the side effects thereof.