JOIN always produce efficient execution path.
How ever to improve your deletion time, create an index on A/C number on the temp table. I hope you have an index on the A/c number in the original table. You may evaluate various option. Probably, a HASH join will be better option and full table scan on the original table may yield better response time.

Also remember that after deletion, there might be a lot of holes in the indexes. Hence, you must recreate the indexes on the original table.