Do I need to open the upstairs fireplace flue to have a fire in the fireplace downstairs?

I rent a room in the lower floor of a student house. My room has a brick fireplace, as does the living room upstairs. It's freezing down here and I would like to have a fire this weekend to warm up our floor (my poor roomie down here has no fireplace and her room is equally as chilly). It would also reduce the heating cost because we could shut our vents and they could lower the heat upstairs. My question is do I need to open both flues in order to have a fire in just the downstairs fireplace? I believe they are traditionally separated but I wanted to be sure first. The last thing I need to do it have smoke billowing into the upstairs!