The Diagnostic Subsytem in the LISA Technology Package (LTP) on board the LISA Pathfinder mission (LPF) will characterise those external disturbances with a potential impact on the performance of the experiment coming from either thermal, magnetic or charged particles perturbations. A correct design of the experiments to measure these effects in flight requires a closed loop analysis that takes into account the dynamics of the test masses, the force applied by the controllers and those noisy terms (coming from sensing or force noise) that enters into the loop. We describe this analysis in the thermal case and we give a first numerical example of the instrument response to controlled thermal inputs.