Here is the actual T-SQL I think this will work:
INSERT INTO [notes]
([projectID]
,[userName]
,[createdDate]
,
,[emailed]
,[attachment])
SELECT [noteID]
, T.matchID as [projectID]
,[userName]
,[createdDate]
,
,[emailed]
,[attachment]
FROM [notes] N, [tempIDs] T WHERE N.projectID = T.projectID