How To Split A Large Transaction?

I have a huge table with ~30G data, and a column needs to be updated. In order to avoid a huge transaction, what I did was setting up a loop, update part of the records in each loop. The query is like following:



Declare @mo smalldatetime
Declare MOs cursor
for
Select [a month] from [a table]

Open MOs
Fetch Next from MOs into @mo
while @@FETCH_STATUS = 0
Begin
exec sp_UpdateColumn @mo
-- PRINT @mo
Fetch Next from MOs into @mo
end
close MOs
deallocate MOs

sp_UpdateColumn is the query that actually does the update, the code is like following:

Create Procedure sp_UpdateColumn @updMoDate smalldatetimeAS
[do some calculation here, store results in a temp table #Temp1]
Begin TranUpdate A set col =b.col from [big table] A, #Temp1 B where [some matching conditions]Commit GO


The BEGIN TRAN and COMMIT lines were meant to break up transaction, however, our database support people still tell me that a huge transaction has generated a GB sized log file that blocked the drive. Unless the transaction wasn't really splitted this should not happen. Can someone help me take a look at the code and tell me is there anything wrong? Thanks