The one time when this happened to me (they thought I was ineligible for a refundable tax credit; I mailed them both a check for the amount they thought I owed

The one time when this happened to me (they thought I was ineligible for a refundable tax credit; I mailed them both a check for the amount they thought I owed and proof that I was indeed eligible for the tax credit) the IRS did actually compute and add interest to the refund check! Sure, the gov't cashed the check and held on to the money for like two months, but the interest at the end was a pleasant surprise.