No, like a steam engine providing electricity for the vapour compression refrigerator. Since I don't know what a pressure vessel is and how it makes energy, and you didn't tell me, I replaced it with a steam engine because I know it.
So, cold water gets heated, the steam is used to drive a rotor, which is converted to electricity, which is used to power the vapour compressed refrigerator, which cools the water back down. Classical perpetual motion machine. If this worked, we wouldn't go through all the trouble to use solar, nuclear, coal and wind energy.