The temporal aggregate in temporal databases is an extension of the conventional aggregate to include the time oil the range condition of aggregation. It is a useful operation for Historical Data Warehouses, Call Data Records, and so on. In this paper, we propose a Structure for the temporal aggregation with multiple range-condition attributes, called the ITA-tree, and an aggregate processing method based on the structure. In the ITA-tree, we transform the time interval of a record into a single value, called the T-value. Then, we index records according to their T-values like a B+-tree style. For possible hot-spot situations, we also propose an improvement of the ITA-tree, called the eITA-tree. Through analyses and experiments, we evaluate the performance of the proposed method. (C) 2004 Elsevier Inc. All rights reserved.