Looks like nighttime temps can dip on avg to 39ºF in May, with daytime temps in mid-high 60s F.
This may be helpful, from NOAA. I use it all the time when heading somewhere:
You can always get helpful info on the USDA pages, too, for national forests. Here's the one for:
Lincoln National Forest
I've camped in the mountains out that way both by van and trailer/RTT in years past.
As for heat while boondocking, a lot depends on what vehicle you're traveling in, if alone or with family, and if tent camping or RV or. . .
I'm always fine, whether in van or RTT, with just a
Mr Buddy Heater to warm things up a bit before sleeping (I don't like running it all night), then depending on
jungle blankets and my cheap Coleman sleeping bag spread open. Even in sub-freezing weather and storms, has worked really well for me. Warm clothing for early mornings and after dark is advised.
I bet you'll enjoy White Sands. Last time I was out there it was all closed up because of the govt shutdown, but we found plenty to do in Silver City, Alamagordo, Las Cruces, and Gila NF.
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