Abstract.Results of solving problems of simulating temperature fields in domains with movable boundaries of characteristic zones of intensive physical-chemical and thermomechanical transformations to be realized in materials upon high-temperature heating have been presented. Intumescent fire-protective coatings based on organic and mineral materials are the object of study. Features of numerical realization of input equation systems taking into account, in particular, a dynamics of considerable increase and subsequent decrease of the intumescent layer thickness have been considered. Example calculations for structures of metal and wood protected with various coatings are given. Results of calculating twodimensional temperature fields in polymer composite square-shaped structures with internal cruciform load-bearing elements have been presented. The intumescent coating is arranged on the external surface of a structure. The solution of the above-listed problems is of important significance to provide fire protection of different-purpose structures and products.Problems of simulating temperature fields in materials suffering physical-chemical and thermalmechanical transformations upon heating under the action of high-temperature gas medium fall into a number of important heat-exchange problems. Such materials include, for example, intumescent fireprotective coatings designed for fire protection of different-purpose structures and products of metals, wood and polymer composite materials.Experiments for structures with fire protection, when simulating real fire conditions, are laborconsuming and high-cost. In many cases, moreover, they are accompanied with difficulty solved physical-similarity problems. In this connection, a mathematical simulation of complex processes under investigation is expedient. When developing corresponding techniques and calculation programs, it is necessary to take into consideration that heating of materials under study is accompanied with a boundary movement of observable zones of physical-chemical and thermalmechanical transformations. The simulation should be carried out taking into account the formation processes and change dynamics of the thickness of the swollen material layer that, in essence, is the protective layer of the surface of some object under fire conditions. Till the present time, a general a Corresponding author: a.n