Tim:
At any rate, it's unusual to use the case as the heatsink, unless you're buying one of those expensive silent PCs. It's the fans that do the heat dissipation.
g:
if you do not want to cremate the cpu, be sure you have a fan or two.
Some don't have any, nor need any. They use heatpipes to shift the heat from the CPU, to massive heatsinks (the whole side of the case, with thick metal) that can absorb a lot of heat.
The usual tiny CPU heatsinks aren't the world's best radiators. They do need fan forced cooling, at least since about the 386 era. And, even with it, they're not always that brilliant. Put your fingers on some of them, and they're still painfully hot, despite a fan whizzing its heart out. And they're very susceptible to mechanical failure, and clogging with dust.