Well, in general, you take the liner that comes with the boot. And I wouldnt recommend doing anything otherwise. Putting a Brand X liner in a Brand Y boot could lead to some serious fit issues, possibly even compromising the insulation by squeezing your foot or creating voids where moisture and cold air could be trapped.
La Sportiva Nuptse boots
Nuptse mountaineering boot
That said, most liners have some combination of closed- and open-cell foam made of polyethylene or a material called Alveolit. The popular Koflach Arctis Expe (US$365; www.koflach.com), for instance, has a heat-moldable liner that comes with both materials. Thats ostensibly to help with durability, as the knock on Alveolit is that it doesnt last as long as lesser (and admittedly not as warm) liners. That said, the Arctis Expe is a proven boot, good for temperatures down to minus-60-degrees Fahrenheit.
La Sportivas Nuptse mountaineering boots (US$525; www.sportiva.com) would be an interesting choice as well. The boot uppers are made with five-ply coated nylon, leatherette and leather, not plastic, for a softer feel. The liners are high-density foam with an aluminum coating that reflects heat. I havent tried these but theyre said to be exceedingly warm. But fit is very important on these boots. You cant just buy a big boot and let your feet slop around, as you can with some plastics.
Scarpas Inverno (US$279; www.scarpa.com) remains a great buy in a good, all-purpose plastic mountaineering boot. Its standard liner is made from EVA foam (not heat-moldable). But for another $150 you can buy high-altitude liners made with Alveolit foam. Dont expect too much use of them, however, as they simply dont hold up that well.
Its a little hard to say which of these would be warmest" as there are so many variablesthe temperature, snow or ice conditions, your condition, socks, and on and on. But the boots I mention, plus many others, are meant for intensely cold conditions. Combined with the right socks and overboots, there are very few places on the planet where you couldnt go.
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