I don't have an answer to your question. But what I would try is putting your machine in the refrigerator running and record what happens. It would beat being in a tent at 37 degrees and then finding out there is a problem. I'm betting the 41 degree limit was arrived at by the lawyers not the engineers.
Back in the day of film cameras, they got really sluggish at anything less than around 35F. Any further, and it was like you had a timer set. You had to use a tripod in order to get decent shots. I once had to shoot (photograph) a flag ceremony when it was about 5F. I had to use two cameras. One would be tucked under my shirt and jacket and the other was on the tripod. If I needed quick shots, I whipped out the one under my shirt.
While CPAPs are much further advanced than cameras, they still do have moving parts. Then there's the type of soldering or adhesives used. Some do not tolerate temps lower than a certain amount or they pop off. Same with high temps. (my brother just did a field trip where the company had put meters into steam pipes but didn't say that's where they would be going and did their own calibrations. The adhesives came lose and the meters failed.)
On the whole, though, I would assume anything above freezing would be fine. Less than that and stuff starts happening. You might be able to put the machine in the sleeping bag with you but only if the incoming port was allowed fresh air. Which defeats the purpose of keeping it warm. The simplest solution would be to get those gel heating packs that you squeeze and it generates heat. Put one near the intake and another on top on a towel. Between the two, it should work. As long as the pack was safe to put directly on your skin, it *should* be safe enough for the machine.
Hey! Know anyone who works at a convenience store? Those beer coolers are kept just a few degrees above freezing. Put one in there, run it, then use a manometer on it to see how it goes.
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Thanks for the good replies. I was able to do new searches based on your various ideas.
Here's the short story. I can give the long one if someone is interested.
It seems that every cpap machine has a low temperature spec = 41F. This suggests that it's not the machine, it's the process.
Looking further, we find claims that temps below 41F are likely to result in condensation in the tube, since "some of the exhalation makes its way into the tube". This can lead to rainout. So, I'll tentatively take this as the reason for the spec. I see that one can buy tube sleeves to keep the tube warmer.
One guy was planning to use his cpap in sub-freezing weather, but was fearful of breaking the machine, so he bought a used one for this purpose. It sailed right through the cold night with no problems.
During the searching, I encountered a question on a supplier's website, "Why are your units so cheap?". Answer: We sell reconditioned units which meet original specs. Medicare-related fed regs keep the price of new units artificially high, but those regs do not apply to the after-market.
I'm toying with the idea of running mine in the refrigerator, but I'm currently having courage issues.