Global warming is more about the "greenhouse effect" (certain gases like CO2 helping to trap in infrared energy) than it is about individual sources of infrared energy.
The reason why AGW is such a big threat is because it causes Sun's energy output to be trapped more effectively. Even if we collectively dumped every single joule of energy we generated into the environment, we'd still be miniscule compared to that.
Note however that it can have local effects - e.g. if you use water from natural sources to cool your datacenter and then dump it back into the environment, it can easily raise up the water temperature enough to affect the ecosystem around. This can also have far-reaching effects - e.g. say you do that in a river where salmon from far away comes to spawn...