Thompson has put in some impressive displays recently and Albion were keen to extend his stay until the end of the season, which the Millers agreed to.
Meanwhile Rowe made his debut for struggling Skrill North side Stalybridge in a 2-0 defeat at home to Telford at the weekend, and will stay for a month to get first team games uner his belt.
MillersMAD wish both lads the best of luck in their continued development.