Temporary tablespaces are shared objects and they are associated to an user or whole database (using default temporary tablespace). So, in RAC, temporary tablespaces are shared between the instances. Many temporary tablespaces can be created in a database, but all of those temporary tablespaces are shared between the instances. Hence, temporary tablespaces must be allocated in shared storage or ASM. We will explore the space allocation in temporary tablespace in RAC, in this blog entry.
In contrast, UNDO tablespaces are owned by an instance and all transactions from that instance is exclusively allocated in that UNDO tablespace. Remember that other instances can read blocks from remote undo tablespace, and so, undo tablespaces also must be allocated from shared storage or ASM.
Space allocation in TEMP tablespace