i use an insulated cooler for the MLT, but I don't put the lid on and i don't stir my mash. I circulate through a HERMS coil to maintain temps.
I have checked the temp gradient in most of my brews by using a probe at the point where the wort comes out of the heater and back into the MLT, another probe thermometer in a thermowell located in the middle of the grain bed, and a floating thermometer that is jammed down into the MLT so that the tip touches the false bottom.
I have seen, at most, a 1* temp difference between my three probes.
Ground Fault Brewing Co.