I wouldnt worry about the temp of the mash inside anyways.
Even with an ambient air temp of around 60, I lose maybe a degree or two with my 10 gallon cooler MLT, even with a decent amount of head space(if I am mashing thick or something).
Any attempts to monitor the temp without stirring will be futile anyways because of the hot and cold spots that develop.
Get your mash temp where you want it, shut the lid, and forget about it.
If you are so inclined, measure the temp at the end of the mash just to see how much you lost. I'll bet you 10 bucks you dont do it more than a couple times.