The sun room sounds like a bad idea given its temperature spikes. I'm not an expert though, see below.
In MA I have mine under a table draped in plastic sheeting under my porch. I covered the pots and the top of the soil in mulch. One thing I think I should have done was put boards underneath so that they aren't sitting right on the earth, as I imagine soil could cause the drainage holes to clog.
Does that sound about right? I was half tempted to leave them out to the elements without the plastic, but this how I did it last year and it worked fine (though last year I just used dry leaves rather than actual mulch).
Along with shimpaku, I also have japanese maple, sweet gum, alberta spruce, boxwood, and white pine stored that way.
I've been told that trident maples wouldn't survive in that condition and need an unheated garage in my zone given the freezing, but I believe all these others ones are fine with it. I'm a little iffy about the sweet gum but they sound so vigorous I'm rolling the dice.
Anyways, back to the point, I suppose out in nature there are temperature spikes as well (say the 70 degree days we get in February sometimes) but I feel like they'd be more regular and at the whims of the sun in a sun room, as well as more likely to hold the heat for longer.