|MadSci Network: Medicine|
http://www.ussartf.org/heat_related_illnesses.htm spells out how the body generates heat by shivering, and conserves heat by vasoconstriction. Very cold water will cause both of those. If you can cool the patient without triggering shivering or vasoconstriction, you're in business.
The same site recommends giving a salt solution, and mineral water does contain salts. Something like Gatorade might also be good, but in general avoid sports drinks.
Best advice you can get regarding heatstroke, heat exhaustion or hyperthermia is don't get it. If you know you're going to be at risk for it, bring enough water so you can drink until you slosh. And don't wait until you're thirsty to drink -- drink regularly!
Also bring a cell phone if you have one, so you can call for help if you need it.
Try the links in the MadSci Library for more information on Medicine.