How to reduce temperature difference between the second floor and basement?
Is this a central heating system? Adjust the dampers in the basement to full open and close them down on the upper floor, if you have AC you will need to reverse them in the summer or close the lower floors dampers and open the upper floor dampers. I like control dampers on the main ducts to each floor so there are only 2 adjustments, 1 in summer and 1 in winter instead of having to adjust all of them.