Standpoint linear temporal logic SLTL is a recent formalism able to model possibly conflicting commitments made by distinct agents, taking into account aspects of temporal reasoning. In this paper, we analyse the computational properties of SLTL. First, we establish logarithmic-space reductions between the satisfiability problems for the multi-dimensional modal logic PTLxS5 and SLTL. This leads to the ExpSpace-completeness of the satisfiability problem in SLTL, which is a surprising result in view of previous investigations. Next, we present a method of restricting SLTL so that the obtained fragment is a strict extension of both the (non-temporal) standpoint logic and linear-time temporal logic LTL, but the satisfiability problem is PSpace-complete in this fragment. Thus, we show how to combine standpoint logic with LTL so that the worst-case complexity of the obtained combination is not higher than of pure LTL.