How can we prevent the upper floor in a split-level home from getting too warm?
Usually we have dampers to adjust multi level homes in winter pushing more heat down stairs and less upstairs, if there are no main trunk dampers individual room vents usually have dampers or are adjustable. I never recommend totally closing a duct off because I have seen ducts split and flex line blow off when vents were closed too much. Opening the lower vents and partially closing the upper vents will help. 

I have also found that keeping the main fan running in low can also help as the air is moved constantly so the upstairs won't have the heat naturally moving up.