imo full piped AC (or even a stand alone plugin AC/heater combo)would take up to much room plus may be dead noisy during playback. unless the only time your going to use the room is in the middle of the day during summer id go with a radiator. garages get pretty cold at night even in summer causing condensation to form in your AV set up.(not good news)
However this is not the real issue.
As the floor is probably just concrete onto earth there may or may not be a damp proof membrane underneath or even a damp proof course in the wall (dependent on the age and quality of the original build). check this out before you start work because even though the conversion will look great just after youve finished if you cover over the floor with carpet/ tiles/ laminate board this will stop the evaporation of water (from the ground up through the concrete and out through the non air tight garage door). if you prevent the floor from 'breathing' two things will happen, the moisture will travel up the walls and rot your nice new plasterboard filling the room with the sweet smell of mildew and secound what ever you fitted on the floor will build up moisture behind it and will also start to rot.
bad news unless you want to dig up the concrete floor and lay a hung wooden floor with lots of ventilation i.e airbricks (like the rest of your house).
a radiator will go some way to help the room feel like the rest of your house in the short term but will not solve the underlying problem.