The aim of this work is a numerical investigation of the process of high-temperature ignition of an infinite gas-free condensed homogeneous system by an inert hot plate and the process by which combustion passes beyond the limits of the igniting plane. No account is taken of phase transitions and the various thermophysical characteristics of the initial material and the combustion products. The reaction of thermal decomposition of the initial gas-free system is assumed to be a first-order reaction. The process of ignition and propagation of combustion beyond the limits of the ignition source is described by a system of differential equations of thermal conductivity and chemical kinetics. Concludes that taking the stage of heat-source ignition into account does not have a very strong influence on the critical conditions for transition to combustion conditions. Indicates that after somewhat modifying the Zel'dovich qualitative principle of thermal initiation of the combustion of gas by a spark, it may also be used in the case of source initiation of the combustion of gas-free systems.