We study combinations of the description logic DL-Lite_{bool}^N with the branching temporal logics CTL* and CTL. We analyse two types of combinations, both with rigid roles: (i) temporal operators are applied to concepts and to ABox assertions, and (ii) temporal operators are applied to concepts and Boolean combinations of concept inclusions and ABox assertions. For the resulting logics, we present algorithms for the satisfiability problem and (mostly tight) complexity bounds ranging from ExpTime to 3ExpTime.