I have seen this before. It is not clear from your other answers if you have an HG index on each individual column of the join.
e.g. create an HG index on each of T1.ID and T2.ID. Only if they are the only columns already identified as Pkey, Fkey or Akey do you not have to index them, as those are automatically indexed. If the column is part of a composite key, still HG index each separate column.
(You can also add an HG to your search argument if you like).
Can you post a query plan (HTML) with query_plan_after_run = 'off' to see the estimates?
Chris