To make this work the heat vents need to be on the opposite side of the room.
Cold air return basement ceiling.
You do this and i guarantee you that the second floor is going to be much more comfortable year round.
One other caution is to have the cold air.
Have a professional contractor install a cold air return gadget in your basement.
The air flows across the ceiling in the hallway towards a larger cold air return that does extend to the basement furnace.
So turn the cold air return 90 degrees through the wall so that it actually draws the air from the room next to the furnace room or from the hallway of the basement.
This pulls the air across your body.
In the upper stories of the house the return air duct openings on each floor should be approximately equal to the sum of the hot air outlets.
If the supply ducts are high or in the ceiling then the return air ducts or grills should be low on.
If the supply ducts are in the floor then the return air should be located up high.
If they are near the cold air return that s all that will happen is you cycle warm air into the cold air return.
This tool promotes cool air circulation through duct work and other house passageways.
If there is a cold air return on the floor the warm air that would normally tend to collect near the ceiling will be sucked down into the furnace.
By putting the cold air return on the floor it will vacuum up the cold air on the floor and draw down the warm air from the ceiling.