I did something similar years ago (I've now got another drawer with the same problem).....I sprayed a fine mist of water on it just enough to wet it without soaking it, then pushed it back into the groove and put something heavy on top of the bulge and a strap/old belt/string or whatever to hold it in place. Once completely dry it was no longer bulging. Never thought of an iron but I'd be wary of using anything but an old one.
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Yeah don't so this.. completely destroyed the bottom of my drawer even on low heat. Just turn your drawer bases upside down and put them back in and get those little blocks to screw in on the bottom
I did this over 6 months ago on a very badly bent drawer bottom. I was very shocked that it worked and it has not budged at all since! I make sure not to put pressure on the drawer anymore though.