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Noooo not heat. As @31trum said, go to a cobblers. It's the same machine to stretch out width or length or both.
If you want something at home, there are basic shoe stretchers you buy (to use one shoe at a time).
You can also buy the shoe stretcher solution spray. You can cheat by using regular shoe trees wrapped in something (like paper, taped down, covered in a food bag). It's ghetto but will work to an extent. You can try cobblers cream on the inside of the shoe, or leather oil, if you don't trust the shoe stretcher spray.
recommended technique for stretching just for width? I have a pair of Meermins that become painful after more than a couple hours due to my fat feet :(
I have heard of using a hair dryer, but that sounds like it could be risky...