We investigate the problem of measuring inconsistency in linear temporal logic on finite traces (LTLf). In particular, we present Answer Set Programming-based approaches to compute a selection of traditional inconsistency measures w.r.t. LTLf knowledge bases. In contrast to existing works (mostly on propositional logic), these approaches are novel in the sense that they allow to assess logical inconsistency in presence of temporal operators, as offered by LTLf. In an experimental evaluation on real-world data from the area of business process management, we show that our approaches are practically feasible.