This paper discusses some aspects referring to the characterization and modelling of the resilience of distribution systems in the presence of heat waves. The aim is to identify the specific features that can lead to more detailed modelling of the impact of heat waves on the failures that happen in distribution systems. In particular, with heat waves there are differences between the cumulative distribution function of the time to failure in practical cases and in the theoretical reference used for reliability analysis. These differences may be considered to refine the resilience models due to heat waves. Examples taken from real cases are illustrated and commented.