Hi Cheryl -- I'm in a vastly different climate than you are, but since no one else has chimed in here I thought I might as well tell you what I know (which probably isn't much, as far as being relevant to your situation). I use a ventless propane heater in the spring, when I move my seedlings from indoors (under fluorescent lights) to the GH. A 20-lb tank of propane pretty much lasts for what I need, since I try not to put too much outside until our temps get pretty well settled to staying above freezing at night.
That said, my heater isn't a "patio" type of heater -- do they have any sort of instructions about using or not using in enclosed areas? My feeling is that they are made to use outdoors, where carbon monoxide wouldn't be an issue, but I don't know that for sure. And I'm kind of doubtful that a 1-lb cylinder would last long for heating a 10x12' GH, even if you only need to raise the temp a few degrees.
Again, I'm not sure about any of that... but I would definitely research the issue of using whatever you purchase in an enclosed area. I hope someone else will have some more definitive answers for you!
