The solenoid will heat up only when powered - that is, when the solenoid is open and the system is running. It is a "normally closed" solenoid - so when the power to the solenoid is off, it is closed. No need to manually shut off the water supply - that's what the solenoid will do - at least until it fails. Carefully touch that blue part of the solenoid after it has been powered for a half hour and you'll see what I mean.
We have customers use those solenoids in other applications where they will only be powered for short periods of time. In your application, we have a solenoid with built in circuitry that allows it to run cool. You can put your hand on it after its been running for an hour and it is as cool as can be.
Russ