The aim of this paper is first to describe how the reliability characteristics of a component living in a environment with controlled temperature may be modified by taking into account of random cooling system failure. In a quite simple model, it reduces to a step-stress model where the unique time of temperature's switch is unknown and follows a given lifetime distribution. Then standard results obtained by applying parametric cumulative damage models (also known as Sedyakin models) are introduced in the repairable systems theory. To be precise, we model the failure times of a cooling system with a renewal-type counting process with non negligible repair times. The aim is to adapt the model to standard inspection policies for which the system state can only be known through periodic inspections.