It is possible that the mechanism that chances from the hot "channel" to the cool "channel" of the climate control system is not moving all the way...and sorta picking up warm and cool air. Not sure what year your car is, but they used to use vacuum lines to change the flow of air from the heater core and the condenser core. Sometimes you can access this area under the dash...usually under the passenger side of the dash.
Check both passenger and driver side dash board where the door meets the dash. That is where the fuses are.
You did not say which model Buick. On the Century: Front seating area, driver side, under dash, passenger side of steering column, mounted above accelerator cable
under dash on passenger side of vehicle
Bad "blend door" actuator or stuck blend door on the driver's side.
In the engine compartment passenger side.
The 2003 Buick LeSabre has speakers in the doors of both the driver and passenger side. These speakers are generally about 15 inches.
Under (and inside) dash on passenger side.
At the bottom of your radiator on usually the passenger side.
Between passenger front wheel and water pump
Check the following items............... 1. A/C heater controller. 2. A/C heater controller doors.
Check blower motor fuse Check to see if compressor is working
You can find the 2001 Buick Century Oddie control module on the passenger side firewall. The body control module will be near the bottom of the firewall.