This paper presents the Branch Eigenmodes Reduction Method (BERM) applied to the identification of a heat flux in an advection-diffusion model, with time dependent parameters. The treated application is a 2D disc brake whose velocity and thermal solicitations are time dependent. One of the method's strength lies in its ability to greatly reduce the dimension of the numerical problem, while maintaining a satisfying precision on the entire computation domain. In the considered case, the inverse problem difficulties come from the transport phenomena which requires the use of very small time steps for its numerical resolution. In order comply with the on-line identification objective, a filtering technique is used. (C) 2009 Elsevier Ltd. All rights reserved.