The purpose of this work was to investigate experimentally the capacity of passive acoustic thermometry (PAT) for the reconstruction of 1D, time-variable distributions of the internal temperature. Because in the PAT a noise signal is measured, a considerable integration time (about one minute) is required to attain an acceptable error level (0.5–1 K). To optimize the time, an algorithm was proposed to take account of the fact that the temperature satisfied the heat equation. The problem was reduced to that of determining two parameters (initial temperature and thermal diffusivity) of the object under study. The desired parameters were considered constant and were not determined anew after each measurement; instead, their values were refined using all the previous measurements. The proposed algorithm was tested experimentally (where the temperature was reconstructed in a model object, a slab of polytetrafluoroethylene) and investigated by means of computer modeling. The duration of one measurement was about 5.5 s. As a result, an error of the temperature reconstruction of about 0.5 K, acceptable for medical applications, was attained after 30–60 s (depending on the depth) from the beginning of the measurements. After that, temperature distributions can be reconstructed after each measurement without loss of the reconstruction accuracy. The proposed method can be used to control the temperature under a local hyperthermia, lasting 1 min and more, of the human body.