When I have laminating done at Staples, it usually is 6 mils, with gusts up to 7 (depending on what they have on hand in the Copy Center). I've gone as high as 10 mils, but it was very stiff and difficult to cut. Also, the clerk had to run it through the machine twice to get the bubbles out.
I've got some self-seal pouches which are 8 mil, and they hold up surprisingly well. However, I intend to get a laminating machine, as soon as I stumble across a bargain like some of you have described!
Back to the original topic--using an iron. No steam, I assume.
Actually, we have a local player who uses his mom's iron, and his game pieces look great and hold up very well. (I won't mention his name because I'm not sure that Mom knows about the Munzee project.)