Would this sour mash technique work?

So I am looking to try my hand at my first sour mash, and am a little confused on how to do so. After a little reading, I think I will go ahead and do this in a spare corny keg to keep any O2 out. I also have a vial of white labs Lacto B. Could I mash as normal, but instead of doing so in the cooler just mash in the corny instead? Then after it reaches 120 degrees (however long it takes), just add the vial of lacto, seal up the keg and then use it after however many days, assuming this will create a sour enough beer with no off flavors/smells? Any reason why this wouldnt work well? If so, any insight on how to do this easily would be much appreciated!

Seems like it would work splendidly. In fact, you could purge with CO2 a little easier in a keg, which is certainly recommended. And you could pull samples to see how sour it is without too much effort or any oxidation. Win win. Possible negative: cleaning up.

Will it be an issue that the temps will most certainly fall to room temperature? I couldnt imagine a keg holding above 90 for very long in a 75* room...

Insulate somehow? With a pure culture and a closed system it might just go slower. Find a hot spot and stick it there, maybe with a space heater? Just thinking out loud, obviously never tried a keg for this.