Pedant alert – Peter probably means Stress Relief rather than Normalisation because the latter is done at a higher temperature and alters the crystalline structure of the steel.
Stress relieving is done at a lower temperature, 650C rather that 850C, ie just glowing dull red, not bright. It might be worth doing.
Recommended procedure is to hold the steel at dull red heat for 1 hour per 25mm of thickness and then allow it to cool slowly in air.
For a long time I had no trouble machining Bright Mild Steel to the point I thought the bending stories might be old wives tales. And then one fine day a job went completely bananas, proving it's all true! However I've cut lots of BMS without trouble, possibly luck, maybe my usual cutting direction is benign, or perhaps steel is made these days in a way that reduces the problem. If the Radius rod is easy to make, I'd just go for it. If a lot of work is likely to go down the drain due to bending, then I'd heat relieve first, or – more likely – dodge the problem by using Black instead!
Provided the steel isn't overheated, there's no harm in warming it up and letting it cool. And it might do some good. But note 1hr/25mm is demanded for guaranteed results, anything less may be a waste of heat.
Dave