moving air down from cathedral ceiling?

Our house has a high ceiling with a loft. Naturally upstairs is the warmest if not hottest place in the house. The ceiling fan helps but not enough. I am going to install some 4 or 6 inch duct work from the downstairs up thru a closet to the top of the cathedral ceiling. I will use a duct booster fan inside the duct to move air. I was wondering if I should pull warm air down from the ceiling or push cool air up from the floor. I am thinking about moving the cool air up so the hot air will drop. Any thoughts???

MIke