There was a similar question about a balcony.
I don’t think the temperature swings are a deal breaker, but it would depend on your definition of “wood shed” 
. I’ve seen everything from a leaky lean-to to a fully insulated and air conditioned building called a wood shed. I’m assuming your’s is unheated and dry.
At the end of the day, it is an electronic device. If you’d be comfortable storing a computer or appliance there, then it should be fine without any special disassembly. There are electronics inside the linear modules; if you don’t think it’s safe to store the controller, I wouldn’t store the linear modules there either.
Assembly isn’t too bad for the occasional use. If you deem your wood shed too damp for electronics, perhaps you’d be ok disassembling the unit and storing it in the box.