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
TEMP tablespaces are divided in to extents (In 11.2, extent size is 1M, not sure whether the size of an extent is controllable or not). These extent maps are cached in local SGA, essentially, soft reserving those extents for the use of sessions connecting to that instance. But, note that, extents in a temporary tablespace are not cached at instance startup, instead instance caches the extents as the need arises. We will explore this with a small example: