Abstract: In the furnace (10) for the high-temperature processing of materials with a relatively low dielectric loss factor (tan .delta.) by heating the material by absorption of microwave energy in a resonant cavity (16), a uniform energy intensity of the microwave field is to be achieved for example by irradiating the microwave energy over a broad band and/or by varying in time the frequency of the irradiated microwave energy. The resonant cavity (16) and the radiation source (13) are tuned to each other such that the relation: (V/.lambda..sup.3). B.gtoreq.20 is satisfied. V stands for the volume of the resonant cavity (16), .lambda. for the wavelength of the microwave radiation and B its band width. V/.lambda..sup.3 equals at least 300 and the clear dimensions 1x, ly and lz of the resonant cavity (16) in the direction of the co-ordinates x, y and z are approximately equal to the cubic root of V. The wall (16.sub.1 to 16.sub.