Normally you always have place at the bottom (or top) of your case.
Since your case has feet, either of the 2 options should work fine. I prefer the bottom, since that is the cleanest option for me. Much space, to work with & no drives, cables in the way.
What you always need to do when using something double is to make large holes in the case, buth that's always better than building an xternal box
So how i would see it:
--- double fans to suck fresh air trough the heatercore in the case
--- heatercore mounted above the hole
--- bottom of case (standing on his feet so that there's enough clearance) with large hole for the heatercore to suck air trough and dustfilter (cleans easier)
Normally the fact that you have hotter air inside you case doesn't make that much of a difference since that air will be pushed out by the new air being sucked in.
When you mount your rad on the top you won't have this problem, but you'll loose a lot of space.