Steps to open database without a backup of the temp tablespace in place. (Or with any other tablespace missing.)
Note: If you are using Oracle9i, use SQL*Plus instead of Server Manager.
Starting from a closed database:
Connect as SYSDBA. Mount the database.
SVRMGR> STARTUP MOUNT PFILE='{location_of_pfile}';Offline drop the datafile.
SVRMGR> ALTER DATABASE DATAFILE '{full_path_file_name}' OFFLINE DROP;Open the database.
SVRMGR> ALTER DATABASE OPEN;Drop the tablespace.
SVRMGR> DROP TABLESPACE {tablespace_name} INCLUDING CONTENTS;Recreate the tablespace.
SVRMGR> CREATE TABLESPACEDATAFILE '{full_path_file_name}' SIZE {size_in_bytes};