What is the best way to heat and air condition a small (10 x 10) room above my garage. It is a second floor laundry room which I constructed in dead spaceabove the garage and family room. It would be very hard to install duct work from the main FHA system. I am hoping to heat and air condition it separately. What are your thoughts?

There are several brands of small uni-vent systems that vent through the wall and provide both heat and a/c. Don't even think of trying to connect to you existing HVAC. This room will be cold in the winter and hot in the summer if you go that direction. It need to be a totally separate system. Zoning would not be that effective either. Unfortunately I can't find my list of these systems but I will continue to look. There are several HVAC guy on this post each day and I'm sure they'll help.
Please rate my answer so I'll know if I helped you. Good luck.

There are air conditioning units sold that vent out a window and will service l000 sq. ft. That may be an answer for that problem.

Mitsubishi Mr Slim heat pump is a very nice unit, quite pricey though. There are many through the wall units like you see in hotels and retirement communities, and many are heat pumps, gas or electric.

Okay... heat pump. Can't you get the small l000 sq. ft. units from sears as we do here? They are vented in a window. They are $150. Cdn. plus taxes. Great for seniors with small incomes and retirement homes.

Tickle, the Sears unit does not heat and cool for $150. I believe what you picture isn't anything more than a window air conditioner. Tigertwo want heat too. Northernheat named the unit I was thinking about, Mitsubishi.

Check out the Samsung mini split ductless. Inside part hangs on the wall, make a small 2 inch hole in the wall to get freon lines and condensate lines out. Best of all SEER is 20.

There are several brands of small uni-vent systems that vent through the wall and provide both heat and a/c. Don't even think of trying to connect to you existing HVAC. This room will be cold in the winter and hot in the summer if you go that direction. It need to be a totally separate system. Zoning would not be that effective either. Unfortunately I can't find my list of these systems but I will continue to look. There are several HVAC guy on this post each day and I'm sure they'll help.
Please rate my answer so I'll know if I helped you. Good luck.

Thanks for the help. I think I was on the rignt track. Can I vent a through the wall unit into dead space? Or, do I have to vent the unit to the outside of the house?

If you are using NG or propane you need to vent outside with an appropriate stainless steel double wall pipe. One that is rated for this application. They are not cheap, about $275 for a kit.