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Some results are presented from investigations studying the process of inversion of multispectral microwave radiometric data to determine the subcutaneous temperature distribution in biological tissues. A transmission line concept is used to model a three-layer planar configuration as typical for the tissue composition of a human upper arm (skin-fat-muscle). Computer-simulated data are generated at 3, 5, and 10 GHz using the Rayleigh-Jeans approximation and the radiative transfer approach. Starting from a characteristic temperature profile, the radiometric data set is inverted to yield reconstructed values of the profile. Using the process of stochastic inversion, it is shown how to compromise between penetration depths, temperature resolution, and confidence level of the temperature values retrieved.