Which of the following is NOT true about thermoregulation?

Contraction of arrector pili muscle facilitates cutaneous vasoconstriction (constriction of the blood vessels), while relaxation facilitates vasodilation (dilation of the blood vessels). Cutaneous vasodilation cools the body by allowing heat to be released through skin, while cutaneous vasoconstriction warms the body by restricting blood flow in the skin. Production of sweat by the eccrine glands facilitates cooling of the body.