What is BAT?
Regular exposure to heat, and especially exercising in the heat, causes your body to adapt. Capillaries near the skin surface expand and move closer, allowing more heat to escape. You sweat more easily and at higher volume. Total blood volume increases to maintain adequate blood flow to muscles and organs when blood has to flow to the skin (this is part of the reason a non-adapted person gets so tired working in the heat--blood flow is diverted away from the muscles to dissipate it). You also excrete less salt into your sweat so you don't get depleted of electrolytes as easily.
Full adaptation takes from a few weeks to a few months depending on your physiology and how often/long/hard you play outside.
EDIT: http://www.washingtonpost.com/nation...U_graphic.html is a nice infographic explaining the process.