I would try:

Update LT Set LT.FileCreatedDateTime = Updated.FileCreatedDateTime, LT.FileType = Updated.FileType, LT.SourceFileName = Updated.SourceFileName

FROM Updated inner join ImageCostFileImportLog LT on LT.RecordId = Updated.RecordId

The advantage of this is it still works if you update the data table with a batch query, your method will only work if you update one record at a time.

Not sure you need the tranaction bit, triggers use an implied transaction and transactions can be tricky to get right

Philip