Wouldn't that cool it too fast, and maybe cause cracking?
I have heard to put the damp cloth in between the tacks, so as to help cool the metal and prevent distortion. This still allows the taks to cool naturally in the air.
Just my 0.02p
Using water makes the weld brittle it can crack not always.
Get a large /or thick plate chuck that on top or hold on the weld, no water needed.