Question

SELECT
    a_fees a
    a_temp b
SET
    b.fee_source_id = a.fee_source, 
    b.filing_date = a.filingdate
WHERE
    b.fee_id = a.fee_id;

Answer 1

MySQL syntax for a multiple table update:

UPDATE a_fees AS a, a_temp AS b
SET a.fee_source = b.fee_source_id, 
    a.filingdate = b.filing_date
WHERE a.fee_id = b.fee_id;

See it working online: sqlfiddle

Using an INNER JOIN:

UPDATE a_fees AS a
INNER JOIN a_temp AS b
ON a.fee_id = b.fee_id
SET a.fee_source = b.fee_source_id, 
    a.filingdate = b.filing_date;

See it working online: sqlfiddle