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I think I would also consider the A/C unit that Syntyr recommended. I would put a turbine type exhaust on the roof and then route the exhaust hose to the roof outside of the bedroom area.

An alternative that might be too expensive in the long run might be to find the duct that provides A/C to the bedroom and install a section that blows into the garage. It would probably be the cheapest (if it can be done) construction wise but the electricity cost on the main A/C unit might be too high. Might even need to get a larger home A/C for that to work.