Isn't there anybody who has done it that way?
Yeah I've done this. I just used double-sided sticky tape to fix the power brick to the metal of the case - this was a desktop-format HTPC case, so it was sat on a horizontal surface - the tape wasn't supporting it just stopping it shifting about. For mounting on a case side-wall you might need to get more creative.
The bricks do give off a bit of heat but not so much that it's remotely a problem in my experience. They're inherently smaller than an ATX PSU so there's a fair bit of room around them if you fit them in the same location, and by definition the amount of power being drawn by the whole kebang isn't particularly large.
It all depends on your case really, if it's fairly roomy I can't see there'd be a problem putting the brick inside the case.