A rigorous three-dimensional electromagnetic model predicting the complete field distribution in the space interior to the 'coaxial TEM' applicator is presented. The applicator consists of a radiating ring aperture, with a given electric-field distribution in the wall of a hollow circular cylinder. The method of calculation employs the spatial Fourier transform of all field quantities with respect to the axial co-ordinate, after which the field equations are solved in the spectral domain. Subsequently, an inverse Fourier transform is carried out to compute the quantities that are of interest to the optimum clinical deep-body hyperthermia system. Numerical results for a number of representative applicator configurations are given. The present results are compared with the ones that are obtained by a model based on the far-field approximation of a distribution of dipole sources located in the ring aperture.