The commissioning and the exploitation of the LHC require a good knowledge of the stability margins of the superconducting magnets with respect to beam induced heat depositions. Previous studies showed that simple numerical models are suitable to carry out stability calculations of multi-strands cables, and highlighted the relevance of the heat transfer model with the surrounding helium. In this paper we present a systematic scan of the stability margin of all types of LHC cables working at 1.9 K against transient heat depositions. We specifically discuss the dependence of the stability margin on the parameters of the model, which provide an estimate of the uncertainty of the values quoted. The stability margin calculations have been performed using a zero-dimensional (0-D) numerical model, and a cooling model taking into account the relevant helium phases which may appear during a stability experiment: it includes Kapitza thermal resistance in superfluid He, boundary layer formation and heat transfer in He I, and considers the transition from nucleating boiling to film boiling during He gas formation.