Check out:http://www.suzuki-forums.com/suzuki-vero...
Quoted responses:

"The most common issue that I as a suzuki technician encounter with the heater and A/C system not switching hot to cold or vice versa is....the control cable that moves the damper door to either allow heated or cooled air breaks and does not move the door at all so whichever position it breaks in ....there it remains.There is no TSB that I know of for this but its quite common .Hope this helps .

Ricky"

AND...

"My 2004 verona would not get any heat. The heater hoses under the hood were both hot meaning that there was heat going to and coming out of the core, not plugged. There are six screws holding the glove box in place and a rubber bumper on each side of the box that you have to push in towards the center of the box to lower all the way to get at the bottom screws. Once that is out of the way you can see the white nylon control arms for the blend door. Turning my heater knob would pull the cable to the closed (cold) position but upon turing the knob to heat the cable just got slack. My guess is that there was a spring connected to the cable arm to pull it into the heat position but must have fell off somewhere. I placed a small spring onto the cable arm and attached it to a nearby screw at the other end. The door now is pulled to the heat position and turning the knob to cold stretches the spring but that works fine. A lot cheaper than going to a dealer. Heck! I would be willing to repair these all day for 1/4 of what the dealer would charge! :-)"

I'm going to try this one. Hope it helps you too.

I also found some info on Blend door Service at:
http://www.autozone.com/autozone/repairi...
(May need to register to create a user-id Check out: http://www.suzuki-forums.com/suzuki-verona-chevrolet-epica-daewoo-magnus/12120-heater-issue.html Quoted responses: "The most common issue that I as a suzuki technician encounter with the heater and A/C system not switching hot to cold or vice versa is....the control cable that moves the damper door to either allow heated or cooled air breaks and does not move the door at all so whichever position it breaks in ....there it remains.There is no TSB that I know of for this but its quite common .Hope this helps . Ricky" AND... "My 2004 verona would not get any heat. The heater hoses under the hood were both hot meaning that there was heat going to and coming out of the core, not plugged. There are six screws holding the glove box in place and a rubber bumper on each side of the box that you have to push in towards the center of the box to lower all the way to get at the bottom screws. Once that is out of the way you can see the white nylon control arms for the blend door. Turning my heater knob would pull the cable to the closed (cold) position but upon turing the knob to heat the cable just got slack. My guess is that there was a spring connected to the cable arm to pull it into the heat position but must have fell off somewhere. I placed a small spring onto the cable arm and attached it to a nearby screw at the other end. The door now is pulled to the heat position and turning the knob to cold stretches the spring but that works fine. A lot cheaper than going to a dealer. Heck! I would be willing to repair these all day for 1/4 of what the dealer would charge! :-)" I'm going to try this one. Hope it helps you too. I also found some info on Blend door Service at: http://www.autozone.com/autozone/repairinfo/repairguide/repairGuideMain.jsp (May need to register to create a user-id