Du kan göra detta
CREATE TABLE TableA_TMP AS
SELECT * FROM TableA;
ALTER TABLE TableA_TMP ADD id_new int;
UPDATE TableA_TMP A INNER JOIN TableB B ON lower(A.title) = lower(B.title)
SET id_new = B.id;
RENAME TABLE TableA TO TableA_backup;
CREATE TableA AS
select id_new as id, title,.... from TableA_TMP;