We present an architecture for query processing in the relational model extended with transaction time. The architecture integrates standard query optimization and computation techniques with new differential computation techniques. Differential computation computes a query incrementally or decrementally from the cached and indexed results of previous computations. The use of differential computation techniques is essential in order to provide efficient processing of queries that access very large temporal relations. Alternative query plans are integrated into a state transition network, where the state space includes backlogs of base relations, cached results from previous computations, a cache index, and intermediate results; the transitions include standard relational algebra operators, operators for constructing differential files, operators for differential computation, and combined operators. A rule set is presented to prune away parts of state transition networks that are not promising, and dynamic programming techniques are used to identify the optimal plans from the remaining state transition networks. An extended logical access path serves as a "structuring" index on the cached results and contains, in addition, vital statistics for the query optimization process (including statistics about base relations, backlogs, and queries-previously computed and cached, previously computed, or just previously estimated).