One obvious way is if it blows the warm air across the A/C's heat sensor, triggering it to do the actual cooling.
Another is if it pushes the heat toward areas of weaker insulation and away from areas of stronger insulation. If the outside is cooler than the inside, then the temperature will leak out more rapidly. If the outside is warmer than the inside, then the warmth will leak in more slowly.
Another is if you're in building and where a vaulted ceiling fan is pushing floor 2 heat down to floor 1. My last house was like that, and I kept the fan on constantly because the floor-by-floor difference was enormous.
Another is if the temperature was not evenly distributed within the room's bottom (eg. because one wall is an exterior wall, or one shares a wall with the kitchen, or there are electrically powered devices in there acting as heat sources). Redistributing will directly cool those parts at the expense of parts further away.