Sorry it took me so long, but I found the material I wanted to link in my earlier post.

Dr. Doug Casa, PhD, is considered one of the most up-to-date experts on exertional heat stroke. Here is a video of Dr. Casa at a seminar. There are more videos with Dr. Casa on YouTube to peruse too.

The Korey Stringer Institute is an extension of the University of Connecticut and is dedicated to research and prevention of heat injuries. Dr. Casa is affiliated with the KSI. Check their site for tons of info.

Specifically from this page at the KSI:

"Myth: 'Peripheral Vasoconstriction (PVC) delays cooling'

Fact: While PVC may occur during cold water immersion (CWI,) it is greatly overshadowed by the great conductive and convective thermal transfer which cools the body rapidly. Furthermore, PVC certainly occurs when a normothermic individual is placed in a cold water bath. Although PVC may minutely increase core body temperature initially, even in a EHS victim, a rapid decrease in body temperature will immediately follow.

Myth: 'Shivering delays cooling'

Fact: Similar to PVC (peripheral vasoconstriction), shivering will certainly occur when a normothermic individual is placed in a cold water bath. However, this is seldom the case with a hyperthermic individual. Research shows that powerful rapid cooling will still occur in hyperthermic individuals with few occurrences of a shivering response.
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Lastly, remember this nugget: "today's heat illness started with yesterday's training". Heat injury is a cumulative thing; you are not out of the woods after the initial cooling. Heat injury has been shown to incite an inflammatory response in the body that takes time to recover from. If you push yourself day after day in the heat, you are risking heat injury more than you think, especially if you do not sleep in cool conditions at night.