Yes, your solenoid is 24 volts AC and 60 hz.
There are also two types of solenoids: "continuous duty" and "intermittent duty". Judging by how quickly yours got hot I'd say you have an intermittent duty type. This means it is only designed to be powered on for no more than 30 seconds, then off for at least ten minutes (lest it burn up or catch fire!).