Can anyone tell me how to effectively use my thermostat?

I just moved to an apt building and with this warm weather plus being pregnant, the heat can become overwhelming. During the day I don't mind it because I'm not home, but at night I like to sleep with the air conditioner really cold. I set the temp for 68 or below on cool and even after 4 hours the thermostat still says room temperature at 72. Isn't the room temp supposed to go down.