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Multidimensional data warehouses and OLAP systems do not provide adequate means for dealing with changes in dimension data, changes appearing frequently in dynamic application areas such as current business systems. As data warehouses and OLAP tools serve as decision support systems they have to reflect such changes. Temporal data warehouses propose sophisticated modelling tools for covering any changes in dimension data but cannot be used with current OLAP systems. In this paper we show some techniques to incorporate temporal dimension data into multidimensional OLAP systems. In particular we show how to superimpose conventional multidimensional data warehouses with temporal master data, enabling queries to span multiple periods and to return correct answers.