Re: Ventilation/Insulation Quandry
Difficult to pinpoint the exact problem(s).
You mention this room has 3 exterior walls with a direct southern exposure and a window ( though not sure what exposure ) would be a tricky heat gain consideration. If the insulation within the walls and/or the attic is insufficient this would be a problem with contributing to heat gain.
The " vent " works .... sounds like there is only one in this room. Possibly there isn't enough cubic feet per minute ( CFM ) being supplied through this vent. If this vent is furthest away from the HVAC unit it may be too small of a supply. This room may require a larger supply or 2 vents. Is there a return air vent located in this room to help with better circulation of the air?
Bottom line .... sight unseen ... it could be an issue with insulation .... or air supply .... or both.
You might consider calling in someone to perform an audit with an infrared camera to determine weak points for the insulation and to measure the air supply for this room ... based on the heat gain calculations.
Perhaps an awning on the outside of this window may help with solar heat gain for this room.
Just some thoughts.
"" an ounce of perception -- a pound of obscure "