First of all do you have sufficient RETURN air in this basement area? Depending on the layout of these various rooms in this basement you may require 2 or 3 RETURNS. (Normally one is sufficient in a open basement)
Also,do the basement exterior walls have any INSULATION? (r value ?)
if the answer is 'no' to the above questions, then that is the main reason for your problem.
if the answer is 'yes', then you could try running your furnace on a continuous "LOW" speed in the HEATING season. This continuous LOW speed will allow the air to circulate into both areas and in a short time the temperature in the 2 levels will somewhat be close to being equal.
Another idea would to re-locate the T-stat into the basement area. Of course you would have to slightly 'damper' down the supply registers in the upper area somewhat.
If you post back with some answers to the above questions, I, or others may try to help you further.