Heat shouldn't be a problem, at least weather wise. I store my tanks out in the garage, out of the sun, which in the Nevada summers gets up to about 125+ deg. UGH!!! I have never had a problem, and don't think I ever will. However, I am wary of leaving them in the sun for too long. Luckily, the hose that I have is long enough to reach all the way to the end of the driveway without moving the tanks, so I rarely have to. Driving them to be filled is the longest they are ever in the sun.
Go to your supplier and ask to see how they store them. Mine just stores them under cover (usually, not always), flammable gasses out of the sun, under proper cover. But they don't keep them inside in the summer.
Acetylene tanks do have a thermal plug in the bottom of the tank, which is designed to melt out and release the contents in the event of a fire, but don't let go till around 600-700 deg.
Also,
I was always taught to turn off the fuel gas before the oxygen, for two reasons. First and foremost, oxygen is not flammable or poisonous, so letting excess out into the shop is not a big deal. So if you forget to turn it off, well you are out of oxygen, but that's the biggest problem, and oxygen is cheaper. Second, because acetylene is the entire fuel and heat portion of the fire triangle in this equation, once it is gone, there is no more fire. Much safer this way.
-Cody