水 and 湯: water states and pouring
Distinguish water from heated water in everyday expressions and track states before and after heating.
The word for water
水, read みず, means water. コップに水を入れました。 means putting water in a cup.
水を沸かしました。 means boiling water. Distinguish heating from merely transferring water to another container.
Naming heated water
湯, read ゆ, means heated water and also appears as お湯. お湯を注ぎました。 means pouring hot water.
お湯が冷めました。 says that the heated water cooled. It does not give the resulting temperature.
Everyday contrasts and measurements
When 水 and お湯 are contrasted, they usually distinguish unheated from heated water. Do not restrict 水 to cold water in every scientific context.
お湯に水を少し足しました。 means adding a little water to the hot water. Keep the added substance and its destination in the correct roles.
Does お湯が冷めました give an exact temperature?
Show the answer and why
No. It gives a cooling change; a numerical temperature requires separate information.