The internal temperatures of plasticine models and the human forearm in vivo were determined, based on remote measurements of their intrinsic ultrasonic radiation. For passive detection of the thermal ultrasonic radiation an acoustic radiometer was developed, based on a broadband 0.8-3.3 MHz disk-shaped ultrasonic detector with an 8 mm aperture. To reconstruct temperature profiles using the experimentally measured spectra of thermal acoustic radiation a priori information was used regarding the temperature distribution within the objects being investigated. The temperature distribution for heated plasticine was considered to be a monotonic function. The distribution for the human forearm was considered to fit a heat equation incorporating blood flow parameters. Using sampling durations of 45 s the accuracy of temperature measurement inside a plasticine model was 0.5 K. The measured internal temperature of the forearm in vivo, at 36.3 °C, corresponded to existing physiological data. The results obtained verify the applicability of this passive method of wideband ultrasonic thermometry to medical applications that involve local internal heating of biological tissue.