I tried to do this once. Bought 2 of the the weldless bulkheads (cooler thickness) for a valve and a thermometer. Got a rubbermaid 10-gal cooler from lowes.
It worked terribly.
The valve was fine. The built-in hole in the cooler sealed up nicely with the bulkhead, and it was great. I would recommend that part.
The thermometer was a nightmare. I drilled the hole with a hole-saw, went slow, everything looked good. But a crack developed almost instantly around the hole once I filled it with hot water. It leaked like a sieve. The cooler insulation is somewhat... absorbent. It soaked up the hot water and filled the cavity up till it started leaking to the outside.
Basically, I threw it out. If I tried to use it for a mash tun, it would have hot wort getting into the insulation, and the mold would set in instantly.
Bought a new 10 gal round cooler, and just put in the valve. That worked, but it still dripped very occasionally. Not a leak really, but I think some liquid could still get into the insulation past that silicon gasket.
That cooler became my HLT. It holds hot water for me fine, and a little water in the insulation won't cause problems like wort would. I didn't bother with a thermometer, because I think that is hopeless.
I ended up making a mash-tun out of an insulated keggle, and am very happy.
I wish you luck with the cooler MT. But think very carefully before trying to put in a built-in thermometer. There might be other options like a pen-thermometer that you just check every now and then, or a thermo-well with a remote sensor.
