Funny you'd suggested a flat iron, I've wondered about it too.
I got a temperature controlled hot air gun so that I could work out what I was doing (since then I managed to break it), however once you have the knack it's ok with an ordinary hot air gut (at least 2000W).
The mistake I made when I started was going too hot too quick and just scorching the surface layer, the second mistake was not giving it a couple of days to re-aclimatize.
To do it right you should get bored rigid thinking nothing is happening, just when you are about to give up you notice the wood is maybe darkening a tad? Then it starts going a deffinite honey, then brown. All this time you are wafting it about an inch above the wood and you are wishing you'd made a jig to hold the hot air gun.
To do one limb takes about 30-45 mins, that gives you some idea.
The problem is with a jig, you go indoors and start to watch TV and forget while the wood is scorching to a crisp
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The great thing about a hot air gun is you can bend and heat treat at the same time. But leave it clamped up for at least 2 days (I usually try for 3 'cos I know I'm an impatient old git)
I can PM you my heat treating notes with actual temperatures if you get a temperature controlled gun if you want me to.
I still use steam for some jobs, there are pros and cons to both.
Del