The identification of the spatio-temporal variations of a heat flux density field is addressed in this paper. The developed technique combines the use of reduced models (BERM method) with an iterative method of conjugate gradient descent, for which the gradient is estimated by the adjoint method. The application relates to the identification of the heat flux received by a brake pad in a braking situation, for which the mechanical deformation and the phenomena of wear cause the appearance of hot spots that one seeks to locate. The use of two different Branch bases, one for the temperature field and the other for the heat flux, enable to identify rapidly the time-space variation of the heat flux, without any hypothesis on the spatial form on it.