The collapse of building structures after a fire is not uncommon. Taking into account the parameters that affect the elements of the building exposed to extreme temperatures of fire and extinguishing allows assessment of the durability of the entire structure. The analysis of regulatory documents on the survey of buildings and structures after a fire allowed us to establish they lack consideration of such parameters, including the Code of Practice 329.1325800.2017 “Buildings and constructions. Examination rules after a fire”. The decision on the appropriateness of the further operation of buildings after the occurrence of both single and multiple fires is possible based on mathematical modelling of this process, and its software and algorithmic support. The technical objective of the study is to create a universal model for the software calculation of the restoration of structures after fire and fire extinguishing. The object of the study is the fire-related damage and destruction of building structures due to thermal effects. The research method consists in developing a cellular model of a thermally insulated plate based on the localization of the heat source in a certain position above the plate and characterized by the temperature distribution in the cells. The evolution of this distribution is a transition probability matrix that describes the change in thermal conductivity along with the plate in two directions and by the functions of the sources. One of the sources describes the supply of heat to a particular cell (a localized moving source), and the other describes the removal of heat due to heat emission to the environment. As a result of the study, a universal model for the formation of a software calculation for the restoration of structures after fire and fire extinguishing has been developed. The purpose of this model is to establish the residual fire resistance of a building structure after a fire with a minimum calculation time and receive recommendations on the possibility of further operation of the building.