Model-based diagnosis was first proposed for static systems, where the values of the input and output variables are given at a single time point and the root cause of an observed misbehavior is a set of faults. This set-oriented perspective of the diagnosis results was later adopted also for dynamical systems, although it fits neither the temporal nature of their observations, which are gathered over a time interval, nor the temporal evolution of their behavior. This conceptual mismatch is bound to make diagnosis of discrete-event systems (DESs) poor in explainability. Embedding the reciprocal temporal ordering of faults in diagnosis results may be essential for critical decision-making. To favor explainability, the notions of temporal fault, explanation, and explainer are introduced in diagnosis during monitoring of DESs. To achieve explanatory monitoring, a technique is described, which progressively refines the diagnosis results produced already.