You generate heat in your arms when walking, but nowhere near as much as you would if you were chopping wood, rowing/paddling, doing pullups or pushups, etc. In addition, your hands are important instruments - you start to struggle with dexterity before tissue damage occurs and usally take steps to protect them. It stands to reason that we end up with more protection on our arms in our World of hiking, backpacking or camping. But look at what happened in the NFL playoffs last week in Green Bay. Temperatures around zero F, windchills well below that and players were bare-armed yet still slick with sweat. Running, throwing, catching, pushing and grappling generates more heat than walking; and the skin of the arms and legs are used to regulate body heat.
The reason that the hot water bottle works between the legs isn't ironic - the femoral artery that carries oxygenated blood to the largest muscles in the body and the fermoral vein that returns that blood to the heart, both run through the inside upper thigh fairly close to the skin. If you want to artifically introduce heat into the body then this is a great choice, because heat transfer can happen rapidly. Heat pads under the armpits work too for a similar reason.
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