Umm, all energy consumption eventually ends up as heat in the environment. If you are bringing "infinite energy" in from space, you will be dumping infinite heat into the environment. Not exactly good for cooling the planet.
Jesus. Someone failed thermodynamics.
The problem isn't heat in the general sense of the word, it's heat trapped in the atmosphere. Heat trapped in the core of the earth isn't a problem at all, for example. Most human generated heat can be absorbed by matter on the surface and has a negligible impact on atmospheric heat. And if you had enough energy and low cost launch to space you could do things like cheaply send solar reflectors into space.