We consider the problems of computing aggregation queries in temporal databases and of maintaining materialized temporal aggregate views efficiently. The latter problem is particularly challenging since a single data update can cause aggregate results to change over the entire time line. We introduce a new index structure called the SB-tree, which incorporates features from both segment-trees and B-trees. SB-trees support fast lookup of aggregate results based on time and can be maintained efficiently when the data change. We extend the basic SB-tree index to handle cumulative (also called moving-window) aggregates, considering separatelycases when the window size is or is not fixed in advance. For materialized aggregate views in a temporal database or warehouse, we propose building and maintaining SB-tree indices instead of the views themselves.