Suppose that every human being received an air conditioner and a place to plug it in that draws from the nearest power source. Let's not get into the logistics of how, they just do. If they all team simultaneously for a day, would the global temperature change? If so, would it go up or down? And by how much? What about a week? A month? A year? And what about the power supply? Would and when would it fail?
Entropy 101 suggests the net effect on the planetary temperature would be a net increase. All ACs do is move heat from inside a structure to the outside, effectively. Moreover, any machine with less than 100% percent efficiency will generate waste heat, including AC units.
However, the planet is big, the effect of 7 billion AC units, even ran continuously, is tiny compared to the solar insolation.
Basically, what Serban Tanasa has stated. Practically, you cannot do anything on a planet to decrease its entropy, unless you increase the entropy of the universe around it by a larger amount.
(Volume of air cooled by the ACs) * (Temperature difference of cooled air from original room temperature air) < (Volume of hot air exhausted by the ACs) * (Temperature difference of exhausted air by the ACs from original room temperature air)
Basically the ACs are using energy to try and decrease the entropy of the planet on local scales (creating temperature difference inside and outside of the rooms they are working in). But the energy they use for this purpose is wasted into heat, hence increasing the global entropy.
How much temperature would go up, depends on the efficiency of your AC units. The higher the efficiency the lesser they will raise the temperature. Under ideal conditions, the temperature increment will be extremely close to zero, but it can never be absolutely zero.
When the power supply would fail depends on the power generated by your power stations.