Short of any solid gold or diamond-encrusted cases you might find for those with more money than taste, you are probably looking at the most expensive iPhone case on the market: the FLIR One, yours for $350.
The case is, however, a fully-fledged gadget in its own right: a thermal imaging camera. TechCrunch had a play with one, and reported that it has several different modes, making it suitable for use by you and I as well as those trained to read thermal images. It can, for example, be set to highlight as simple binary differences the hottest and coldest heat sources in an image (sample images below the fold) …
While the camera is most likely to appeal to those who need it for professional purposes, FLIR believes there is a consumer market too, for example detecting water leaks behind a wall or seeing where heat is lost from a home in order to beef up insulation.
While $350 might seem a steep price to pay, it seems rather more reasonable when compared to the typical $1000+ price of a standalone thermal camera. The case contains a built-in battery to power the camera, and can also help power the iPhone.