Simple Update Kills TEMPDB Database In SQL2005 64-bit

Following update runs 20 hours till TEMPDB grows up to 400GB and runs out of space with error message:

Msg 1105, Level 17, State 2, Line 8
Could not allocate space for object 'dbo.Large Object Storage System object: 440701391536128' in database 'tempdb' because the 'PRIMARY' filegroup is full. Create disk space by deleting unneeded files, dropping objects in the filegroup, adding additional files to the filegroup, or setting autogrowth on for existing files in the filegroup.

T_PERF_LOC has 30,000,000 rows and T_MASTER_LOC has 2,000,000 rows
There is and index on V_KEY in both tables. CHANNEL_KEY is of Integer datatype and not indexed.
F_MAP function performs simple lookup on very small table (10 rows)

UPDATE A
SET CHANNEL_KEY = OTHERDB.DBO.F_MAP(b.ID)
FROM T_PERF A
JOIN dbo.T_MASTER b
on a.V_KEY = b.V_KEY

Any ideas why?
Thanks