The preferred method of climate control is to use the engine heat to mix with evaporator cooled air. I will bet my last dollar on these two thoughts: An open heater valve, or a stuck open blend door. Check the heat valve's vacuum supply. There are two methods of controlling heater valves. One type valve is normally open, and when the enging starts producing vaccuum the valve is forced closed by the action of atmospheric pressure over the vacuum. The second type of heater valve is normally closed and when the operator selects throughout the valve range, it opens or closes the valve.
Next question for you, is your heater valve operated by a vacuum hose or a control cable? It's an easy diagnosis. Just look at it. Packaging errors sometimes cause you to install a normally open instead of a normally closed valve. The valves look the same, but their default status is opppsite. With the engine running, pull the hose off the heater valve to see if there is vacuum present and verify that the valve moves when the vacuum is applied. If it is cable controlled, have someone inside your car move the temperature selector lever throughout it's range to observe whether the valve is opening and closing. If you still have your old valve, look through it to see if is open or closed. The replacement would have the same default; open or closed. You may have a collapsed vacuum supply hose, or no vacuum at all. The car is almost 10 years old. Replace all the vacuum hoses. Have your helper slide the control lever inside the car while you observe how the valve responds when moving the selector throughout its' range. Then look to make sure that when the manual selector is off, that it corresponds with a closed heater valve.
These are all the things to check. 1). The default status of the valve, 2).Whether it is vacuum or cable controlled. 3). If cable actuated, is the cable free to move from on end to the other of its' operating range? If the valve is vacuum actuated, is their vacuum while the engine is running? If I were there I could check all these things in about 5-10 minutes. You can too.