Hahaha, my first thought was that this thread was about travel irons...I forgot there's a hair implement called a flat iron!
I haven't got experience with flat irons (my hair is straight and generally flat anyway), but I will say that my BabyLiss travel curling iron (they no longer sell the type) was awesome and was the only curling iron I used for about 20 years...at which time I donated it to Goodwill as it still worked well but I'd stopped curling my hair.
It didn't have an external heat control, either, but I never had any trouble with it overheating and it cooled pretty quickly so that it could be packed up.