Since not all the air in the car is being warmed, it sounds like there is a malfunction in both the routing and the heater core. The heater core is a miniature radiator located under your dash behind the glovebox that is used to warm the air for your heater, there is ducting with flaps to direct the air through the heater core when needed, as well as to the different vents. There is also a valve that turns the heater core on and off (under the hood on the heater hose), so it is possible the issue is in the controls (as both the heater core is on, and the air is being routed through it).