It is commonly held in historical geology that Pleistocene extinctions were a gradual process lasting over thousands or millions of years. However, frozen mammoth carcasses found buried in the tundra muck give evidence leading to a different conclusion. Of particular interest is the carcass of the Beresovka Mammoth (1901). An analysis is presented of the temperature drop necessary at the time of its death to leave the mammoth in the state of preservation in which it was found. By using thermodynamic models of the mammoth, it is demonstrated that the animal must have frozen to death in mid-summer by being suddenly overcome by an outside temperature below -150 oF.