Woolly mammoths and the living elephants are characterized by major phenotypic differences that allowed them to live in very different environments. To identify the genetic changes that underlie the suite of adaptations in woolly mammoths to life in extreme cold, we sequenced the nuclear genome from three Asian elephants and two woolly mammoths, identified and functionally annotated genetic changes unique to the woolly mammoth lineage. We find that genes with mammoth specific amino acid changes are enriched in functions related to circadian biology, skin and hair development and physiology, lipid metabolism, adipose development and physiology, and temperature sensation. Finally we resurrect and functionally test the mammoth and ancestral elephant TRPV3 gene, which encodes a temperature sensitive transient receptor potential (thermoTRP) channel involved in thermal sensation and hair growth, and show that a single mammoth-specific amino acid substitution in an otherwise highly conserved region of the TRPV3 channel strongly affected its temperature sensitivity. Our results have identified a set of genetic changes that likely played important roles in the adaptation of woolly mammoths to life in the high artic.