Are you breastfeeding?
If so, then there is no need to give extra water to your baby. Indeed it can cause lots of problems because the baby will fill up on water and is likely not to want enough milk, which in turn means less breastfeeding with the result that it can affect you milk supply.
Dr. Sears discusses this on his web site,
Does my breastfeeding baby need bottles of water? http://www.askdrsears.com/html/2/T023000.asp
Breast milk is itself mostly water and in hot weather, babies tend to go to the breast more often, for short feeds. (Usually lots of short feeds help babies with colic too.)
Best wishes,
SARAH