The femtosecond laser pulse induced desorption of a molecule (NO) from a metal surface (Pt) is investigated by means of open-system density matrix theory. Single- and two-pulse scenarios in the so-called DIMET limit (Desorption Induced by Multiple Electronic Transitions) are considered. Special emphasis is given (a) to a realistic modeling of the temperature profiles of substrate degrees of freedom in response to a laser pulse, (b) to the role of vibrational relaxation of the adsorbate-surface bond, and (c) to a critical comparison of our anharmonic "excitation-deexcitation" approach to the simpler Truncated Harmonic Oscillator model with electronic friction. For the single-pulse case, nonlinear scaling of the desorption yield with laser fluence is demonstrated and found to be in good agreement with experiment. For the two-pulse case, time-resolved correlation diagrams are calculated and interpreted.