Temporal extensions of description logics often lead to a substantial increase in the complexity of reasoning. Nevertheless, tractable extensions of ℰℒ have been developed by restricting the occurrences of temporal concepts. One can even add so-called convex metric temporal diamond operators to ℰℒ, if they are only allowed to occur on the left-hand side of concept inclusions. In this paper, we consider the dual convex box operators for the first time, and investigate the behavior of complex temporal formulas in which convex diamond and box operators can be combined via composition, union and intersection. We demonstrate the intricate interplay between these operators, and present decision procedures for checking subsumption between complex temporal formulas.