The authors consider propagation of burn wave along a one-dimensional system of point heat sources connected by inert heat-conducting elements for periodical and disordered systems. Dependence of burn rate of such systems on burn temperature is determined. It is shown that under certain conditions a steady-state combustion mode in periodical systems becomes unstable and it is replaced by oscillatory modes, which consistently lose stability in the form of doubling period bifurcations. It is established that the burn rate of disordered system is many times less than the burn rate of a periodical system at identical average parameters. Results of modeling are compared with experimental data on combustion of thermite systems.