Why wouldn't a giant AC work? Admittedly, you'd need to connect it to the Earth, not just "point it" at us. But an AC is basically a system that uses energy to move heat around; the trick is building one that puts the warm-air exhaust outside the lower atmosphere and gives it escape velocity.

For instance, as long as we're talking mad science, if we could build a space elevator with a big pool of water at the upper end as its counterbalance, cooled by evaporating into space (and maybe by contact with the upper atmosphere?), with a series of tubes connecting the pool with the sea below, then we could run an AC cycle: send warm seawater up, get almost-freezing water down. Of course we'd need a huge throughput to affect global temperature, but the principle is sound :-)