We consider a simplied model of a coupled parabolic PDE-ODE describing heat transfer within buildings. We describe an identication procedure able to reconstruct the parameters of the model. The response of the model is nonlinear with respect to its parameters and the reconstruction of the parameters is achieved by the introduction of a new vectorial descent stepsize, which improves the convergence of the Levenberg-Marquardt minimization algorithm. The new vectorial descent stepsize can have negative and positive entries of different sizes, which fundamentally differs from standard scalar descent stepsize. The new algorithm is proved to converge and to outperform the standard scalar descent strategy. We also propose algorithms for the initialization of the parameters needed by the reconstruction procedure, when no a priori knowledge is available.