In this paper, we present a computational algorithm for solving an important practical problem, namely, the thermoplastic polymer melting under fire conditions. We propose here a technique that aims at minimizing the computational cost. This is basically achieved by using the immersed boundary-like approach, combining the particle finite element method for the polymer with an Eulerian formulation for the ambience. The polymer and ambience domains interact over the interface boundary. The boundary is explicitly defined by the position of the Lagrangian domain (polymer) within the background Eulerian mesh (ambience). This allows to solve the energy equation for both subdomains on the Eulerian mesh with different thermal properties. Radiative transport equation is exclusively considered for the ambience, and the heat exchange at the interface is modeled by calculating the radiant heat flux and imposing it as a natural boundary condition. Copyright © 2012 John Wiley & Sons, Ltd.