The ability to model time-varying natures is essential to many database applications such as data warehousing and mining. However, the temporal aspects provide many unique characteristics and challenges for query processing and optimization. Among the challenges is computing temporal aggregates, which is complicated by having to compute temporal grouping.In this paper, we introduce a variety of temporal aggregation algorithms that overcome major drawbacks of previous work. First, for small-scale aggregations, both the worst-case and average-case processing time have been improved significantly. Second, for large-scale aggregations, the proposed algorithms can deal with a database that is substantially larger than the size of available memory.