Very little heat, the stain blushes quickly. A hair drier would not be quite enough but a heat gun blushes the wood in seconds, I keep the gun moving. I don't think the back of a bow would be in any danger.
This is a test of the bottle of the iron nitrate I bought and used on my last gun; maple scrapwood, one application of iron nitrate, blushed then a couple of coats of Tru-Oil.