The temperature of water doesn't affect its ability to make up for water losses in your body. However, if water is very hot, you may not be able, or inclined, to drink as much of it as you would if it were cool. Never drink hot water from the tap; it is more likely to contain contaminants such as lead than cold water.
You probably feel thirsty after drinking carbonated water because of its effects in the mouth, not because it is less hydrating. However, carbonation can influence the feedback your stomach gives to your brain and may limit how much you can drink, so you may do better after exercising to re-hydrate your body with plain water.
While we're on the subject of carbonation, I should clear up questions about whether it has a detrimental effect on bones. This concern stems from studies performed in the early 1960s suggesting that drinking carbonated beverages, specifically colas, raises the risk of bone fractures among adolescent girls and older women (former college athletes). No such association was found for non-cola drinks.
Researchers from the Osteoporosis Research Center at Creighton University found that excess urinary excretion of calcium occurred only when the carbonated beverages consumed contained caffeine, but even so, the net loss was negligible. While colas appear to be a concern for many reasons such as their extraordinarily high concentration of sweeteners, carbonation itself is not a problem.
Andrew Weil, M.D.