An ability to noninvasively measure the temperature of internal tissue regions would be valuable for applications including the detection of malignancy, inflammation, or ischemia. The output power of a microwave radiometer with an antenna at the skin surface is a weighted average of temperature in a tissue volume beneath the antenna. It is difficult, however, to translate radiometric measurements into temperature estimates for specific internal tissue regions. The chief difficulty is insufficient data: in a realistic system there are no more than a few measurements to characterize the entire volume. Efficient use must be made of available prior information together with the radiometric data in order to generate a useful temperature map. In this work we assume that we know the tissue configuration (obtained from another modality), along with arterial blood temperature, skin temperature, and nominal tissue-specific values for metabolic and blood perfusion rates, thermal conductivity, and dielectric constants. The Pennes bioheat equation can then be used to construct a nominal temperature map, and electromagnetic simulation software to construct the radiometric weighting functions for any given radiometer configuration. We show that deviations from the nominal conditions in localized regions (due, e.g., to the presence of a tumor) lead to changes in the tissue temperature that can also be approximated in terms of the nominal bioheat model. This enables the development of algorithms that use the nominal model along with radiometric data to detect areas of elevated temperature and estimate the temperature in specified tissue regions.