Of course the logical explanation would be that the thermostat must be set really low. Well, they just recently installed a thermostat in my office, so let me check that:
Ah, so it's set to the max of 85. I'm going to venture a guess and say that isn't connected to anything. So you would think that, at a bare minimum, the A/C wouldn't be blowing anymore if the temperature was 60 degrees:
It's not so much the temperature, but the windchill.