Every store has a thermostat for each A/C unit. Look on the columns throughout your sales floor and offstage areas on the wall. They are small beige squares that might say something like "RTU#".
Corporate controls the A/C. Your store team isn't lying to you. Think about your home, how much does your electricity bill go up when it's warm out? Now think of Targets electricity bill. Millions and millions of dollars, spread across the entire country.
Now remember that what may be comfortable to YOU may be too hot, or too cold to someone else. Target realizes this, and has in place a system that works to keep the store temp and relative humidity between certain set points. I believe it's 65-74°, but don't quote me. As long as your PMT is doing his or her job, there is nothing that can be done about it.