In object-oriented database systems (OODB) with logical OIDs, an OID index (OIDX) is needed to map from OID to the physical location of the object. In a transaction time temporal OODB, the OIDX should also index the object versions. In this case, the index entries, which we call object descriptors (OD), also include the commit timestamp of the transaction that created the object version. In this report, we develop an analytical model for OIDX access costs in temporal OODBs. The model includes the index page bu er as well as an OD cache. We use this model to study access cost and optimal use of memory for index page bu er and OD cache, with di erent access patterns. The results show that 1) the OIDX access cost can be high, and can easy become a bottleneck in large temporal OODBs, 2) the optimal OD cache size can be relatively large, and 3) the gain from using an optimal size is considerable, and because access pattern in a database system can be very dynamic, the system should be able...