Different turtles require different heating etc
Please research the turtle you have and it will tell you what temp the water should be

Well you should not have your water turtle in cold water. It should be heated and no they will no go in shock. its okay.

http://www.answerbag.com/Turtles are reptiles and as such are cold blooded. What this means is that in heated water your turtle will become more active and will have better digestion. This is mostly relevant to fully aquatic turtles, heating the water for turtles that are semi-aquatic, or even tortoises, as they will not spend enough time in the water for it to make that much of a difference.

In general though, turtles are perfectly fine in unheated water, as long as the temperature is not allowed to get below 45 degrees Fahrenheit.