I hope this unleashes the design beast in you and we get a sleek-looking passive case project as result !
I used to play around with more out-there, experimental concepts like that. For example, rooting around my sketchup projects folder, here's one from 2009:
This was intended to be a semi-passive, back-to-back design, using a combination of passive radiators (like you'd find in the back of a refrigerator), and "Phaseplane" vapor chambers (a type of flat, flexible heatpipe) connecting the GPU/CPU to a more typical copper heatpipe heatsink at the top with fans on it. The idea being, during idle you could have the fans turned off and the side radiators would be sufficient to dissipate the heat generated, then under load you could switch on the fans to deal with the extra heat.
The passive radiators were based on a real passive PC case design being developed by a small company at the time, though AFAIK they only ever built them to order as product samples, and I don't think they ever really got it off the ground. The innovation there was not the radiators per se (as mentioned, they're the same thing as used in refrigerators), but a passive pump design rather than an electrically-driven compressor to move the working fluid/vapor around the loop, that was entirely driven by changes in pressure. Silverstone showed a similar sort of pressure-driven pump a couple of years back in an AIO (albeit liquid-only rather than phase-change), though it never did come to market.
Anyway, cases with integrated cooling like this can really only be sold as complete systems, since they require very specific parts. Business-wise, that's a whole other can of worms, which I have no real desire to get into. These days I'm much more focused on designing things that can be used with standardized parts, rather than high concept stuff like this. It's a lot more accessible, and there's still plenty of room for optimization.