There are SOME high temperature paints, notably paints used to paint car engine blocks and those used to paint bar-b-que's. My understanding is that Sherwin Williams makes a line of VHT (Very High Temperature) paints that are very good. But, I expect that the colour selection is very limited. You might get your choice of black, gray, red and maybe some metallic colours.
But, I'd never paint directly onto your limestone hearth because it'll be hard to get that paint off should you (or a future owner of your home) ever want to. You can buy 1 inch thick limestone in slabs (just ask at the brick yards or maybe wherever they make memorials (tombstones). I'd buy a piece of limestone slab to fit over your hearth, and do whatever you want to the slab. Then glue the slab down to your hearth with something relatively easy to remove, like a few dabs of construction adhesive.
You can see what's available from Sherwin Williams in the way of their high temperature paints, but another alternative is to make a "mosaic" instead of a painting.
Because of the limitations of the paints that were available before drying oil paints became popular about 5 to 600 years ago, in the dark and early middle ages, artists would make "mosaics" out of tiny pieces of coloured stone. Nowadays, you could use coloured glass or pieces of coloured porcelain ceramic tile, both of which would stand up to heat, glowing embers and hard scrubbing. Porcelain tile is the same colour all the way through the tile. (regular ceramic tile will have a different colour "biscuit" than the surface of the tile)
Soot would prevent your grouting the mosaic. That's because cement based grouts will dry porous, and they will eventually become stained with soot from the fire. The extremely tiny soot particles will get right into the porous surface of the grout, causing it to look dirty (even after cleaning). You COULD use an epoxy based grout, but I don't know how well epoxy stands up to heat.
Another possible problem would be the sharp edges of broken glass or tile, and I expect that could be dealt with by simply covering the mosaic with a piece of glass. That way, the mosaic itself would never actually get dirty from soot, and plate glass is relatively easy to clean. Also, plate glass is actually pretty strong, and a 10 mm thick (3/8 inch) laid over the mosaic would be quite strong if the glass or tile pieces were of uniform height.
You could do something like:
Or:
Because the art medium is glass or pieces of porcelain tile, the art will stand up to heat and hard scrubbing to clean it. Even the occasional acid wash to dissolve the surface layer of grout which may have been stained with soot.
