Local hyperthermia is increasingly being used for therapeutic purposes, such as tumor ablation. Heat conduction and energy absorption in vivo during the hyperthermic procedure are largely unknown, thus making feedback temperature control highly desirable. Here, a general method for temperature control based on Fourier transformation (FT) of the bio-heat equation is presented, taking into account heat diffusion ( Within the full spectrum of electromagnetic and sound waves, only focused ultrasound (FUS) can be used to generate local hyperthermia noninvasively (1). The local temperature increase may serve a wide variety of medical interventions, such as ablation of tumoral tissue (2,3) or cardiac tissue to treat arrhythmias (4). In addition, local hyperthermia has been suggested for local drug delivery (5-7) with thermosensitive microcarriers (1), control of gene therapy using heat-sensitive promoters (8), and heatactivated chemotherapy or local contrast agent deposition (9,10). Temperature evolution during hyperthermic treatment is a function of heat deposition and heat diffusion. Heat deposition by FUS depends on the local absorption of ultrasound energy and its transition to molecular (atomic) vibration energy. Pure water and blood hardly absorb ultrasound energy. The absorption of ultrasound depends on tissue composition and the ultrasound wavelength. Therefore, accurate quantification of energy deposition by FUS and absorption by tissue is difficult to predict. Heat conduction also depends on tissue composition. Diffusion and perfusion processes may vary locally as a function of tissue architecture and tissue composition. Physiological events such as temperature-dependent perfusion increases may play a role. In case of ablation procedures, tissue coagulation may significantly modify heat conduction as well as energy absorption. As a consequence, heat losses and energy absorption are difficult to predict in advance of the procedure.Optimal control of the temperature-based treatment requires regulation of the temperature. Recent developments have shown that rapid MRI, followed by on-line data processing and real-time feedback to the FUS output, and combined with new temperature regulation algorithms, may provide such control. Salomir et al. (11) described regulation of temperature evolution of the focal point based on temperature mapping and a physical model of local energy deposition and heat conduction. An essential element was the real-time evaluation of temperature gradients near the focal point. This was achieved by on-line calculation of the Laplacian value from the temperature maps. The method performed well under conditions of FUS energy deposit in a small, well defined region. Recently, it was shown that the use of either multiple FUS focal points (using a phased-array FUS transducer (12,13)) or a spatial trajectory of a single focal point (mechanical displacement (14)) may lead to shorter treatment times. However, heat diffusion estimated from the Laplacian value of temperature is ill defined in such ...