Most real-world database applications contain a substantial portion of time-referenced, or temporal, data. Recent advances in temporal query languages show that such database applications could benefit substantially from builtin temporal support in the DBMS. To achieve this, temporal query representation, optimization, and processing mechanisms must be provided. This paper presents a general, algebraic foundation for query optimization that integrates conventional and temporal query optimization and is suitable for providing temporal support both via a stand-alone temporal DBMS and via a layer on top of a conventional DBMS. By capturing duplicate removal and retention and order preservation for all queries, as well as coalescing for temporal queries, this foundation formalizes and generalizes existing approaches.