A lot of people will use an insulated cooler for a mash tun. The insulation helps hold the temperature for the proper amount of time and keep things nice and warm.
I do a lot of BIAB brewing on my stove top and have little difficulty keeping the mash between 153-155f. Consistent monitoring and tweaking on and off the heat is par for the course with all grain brewing in a brew pot. My process requires me hitting a strike temperature around 165f and when the grains bring down the temps, adding more heat as needed. I stir on occasion to prevent dough balls and use a metal colander on the bottom of the brew pot to prevent settling and scorching.
Beer so good, it's frightening.
2014: Seven Heavens Series One: Vilon, Mystic Melomel, Skeeter Pee.