The article presents application of mathematical-physical methods for optimization of maintenance work and/or liquidation of dumps with gob fire. The following problems are discussed: diagnostics of the dump thermal fields, theoretical prognosis of natural cooling of the dump surface by the atmosphere at its interface, problems related to the work security when cooling with water, methods of measuring the temperature and thermal conductivity on the site and problems in relation with the dump rai- sed radioactivity. The diagnostics of the dump temperature field is treated in more details. On the basis of mathematical-physical equations it is possible to determine estimates of about 15 basic parameters characterizing the gob fire temperature and thermal field focal point from the temperature measurement data near the surface in short intervals. The procedure mentioned above is original and the reached theoretical results are utilized as the basic data for optimization the maintenance technical procedures aiming to minimize the negative impact of the dumps on the environment.