It is known that overheating of electrical contacts is one of the most important causes of fires. Traditional analysis of contact heating assumes that its source is transient electrical resistance. In this case, the microstructure of the contact area is not considered. Meanwhile, in reality, any contact of solid surfaces is carried out through individual microcontacts. In the proposed work, computer programs have been created that describe the processes of overheating of microcontacts of electrical contacts. Specialized programs are based on the use of the finite element method and are implemented in Fortran codes. Idealized systems containing regularly spaced contact pads within which Joule heat is generated are considered. The heating of a unit cell is considered. Discretization of two-dimensional axisymmetric space by triangular simplex elements is used. A rectangular computational domain is used. Boundary conditions of the first and second kind, as well as adiabatic boundaries, are applied. Stationary processes are considered. Computer experiments have shown that in the area of microcontacts, heating temperatures exceed the average over the contact surface by tens of times. The influence of overheating on the occurrence of fire danger is discussed. The processes of the formation of an oxide film, which causes the isolation of individual microcontacts, are also considered. It is proposed to use the presented algorithms to predict failures of electrical contacts and when constructing a tree of fire events. The prospects for further development of the physicochemical model of degradation of electrical contacts are considered.