Yeah, what you're looking for, is a case extension, like those found in the phase change coolers, sold comercially.
The problem is that you're not going to find one that fits your case perfectly, unless you get really lucky.
If you weren't in Japan, I'd recomend that you build one yourself. Maybe it's just a stereotype, and I need to be corrected, but I'm betting that you don't have a work area to do this, no tools, and I wouldn't bet that the raw materials are readily available.
Is there such a thing as a hardware store in Japan?
Here in Houston, Texas, USA, I've got at least 6 hardware stores within 1 mile from my house.
