As a first endeavor, the one- and two-dimensional heat wave propagation in a medium subjected to different boundary conditions and with temperature-dependent thermal conductivity is studied. Both the spatial as well as the temporal domain is discretized using the differential quadrature method (DQM). This results in superior accuracy with fewer degrees of freedom than conventional finite element method (FEM). To verify this advantage through some comparison studies, a finite element solution ise also obtained. After demonstrating the convergence and accuracy of the method, the effects of different parameters on the temperature distribution of the medium are studied.