Mash thickness is probably the least important aspect of all-grain brewing. Its importance only comes into play when you get to a point where your MLT can not hold the required volume. So, my quick advice is to stir for a minute, and if that does not bring temps down as the mash stabilizes, then yes, slowly add cool water.
(the long advice is to read my method for hitting mash temps every time - skip to the sections labeled "dough-in" if you are in a hurry.)
https://www.homebrewtalk.com/f36/do-not-fear-all-grain-brewing-primer-247631/
When laying out your brew day, spend 2 minutes and figure out what water:grain ratio will fit into your tun for a desired grain bill.
Use the "Can I Mash It?" calculator here.
http://www.rackers.org/calcs.shtml
FWIW, I use a 5 gallon round cooler, and I can mash 15 lbs or grain at a 1:1 (qts:lb) ratio with no problems (and I automate a mashout through a pump for recirculation prior to fly sparging). 1.25:1 is my favorite number, but sometimes it just doesn't fit, so I adjust accordingly. Anything from 1:1 to 2:1 will work fine.
Joe