The paper is devoted to propagation of a temperature field of the soliton type in a nonlinear rigid heat conductor in which both the free energy and the heat-flux vector depend not only on the absolute temperature but also on “elastic” heat flow that satisfies an evolution equation. This equation together with the energy conservation law lead to a nonlinear coupled system of partial differential equations from which the temperature and elastic heat flow fields are to be found. It is shown that for a one-dimensional case, the system admits a closed-form solution of the soliton type, and the soliton's velocity is uniquely defined in terms of the elastic heat flow at infinity. A qualitative analysis of the solution is also included.