I believe this is the same technique (dye sublimation) that Canon uses in their small photo printer range (Selphy line). Those printers work with ink sheets where the ink is transferred one color at a time (yellow, red and blue). After that, a fourth sheet containing some fixing material is printed over the photo which makes it durable.
Quality is much better than comparable inkjet+photo paper solutions. But it's really expensive...
You could take that in a different direction… find a paper that allows you to wash the ink off it, to make reusable paper…