A novel mesh-free Monte-Carlo method for two-dimensional transient heat conduction in composite media with temperature dependent thermal properties is presented. The proposed approach is based on expressing the solution of the transient conductive heat transfer equation, in domains with temperature-dependent material properties, as a combination of two solutions: Bessel functions and integrals of peripheral temperature. The proposed approach is used to solve transient conduction in composite layered materials with temperature dependent thermal diffusivity. Results are compared against others obtained using a conventional finite element approach. Experimental results for heat transfer in a nonhomogeneous domain (composite layered material) are presented to demonstrate the performance of the proposed approach. 2017 Elsevier Ltd. All rights reserved.