I was thinking of putting a board underneath. Though, I need a find a right size board.
Consider spending $20 on a package of four items on this web-page:
http://www.dlawlesshardware.com/casterwheels.html
It may be that the "enthusiast demographics" of the forums have changed since the last decade, but a lot of us have no misgivings for using various tools in DIY projects to "make things better." This is not a criticism of those who don't, but consider this.
When you buy a product like a computer case, the manufacturer cannot anticipate every single situation of the buyer or groups of buyers. You chose the case because you "like it," but the case was not made only for you.
Some cases, like my CoolerMaster Stacker midtower, come equipped with (little) braked caster wheels, but many ( or most) cases don't.
After my Stacker, I opted to spend less on a case that I like for various reasons despite the fact that some people think it's "butt-ugly:" the HAF 922. I observed a simple fact about it common to most cases without wheels: it has little round rubber (or plastic) feet, attached to the case bottom with 6-32 machine screws.
Most communities, towns -- cities -- have a "metal supply store" somewhere. You can obtain 2"x0.25"x12" aluminum bars, pre-cut to that size (but aluminum is easy to cut anyway with your standard hacksaw and ubiquitous "metal-cutting" blade). You can get a drill-tap kit for 6-32 screws at Sears for $5.
After cutting the bars to the precise case-width, you drill two holes in each one (carefully, precisely) so you can attach each one to the front and rear pairs of holes used for the rubber feet, using slightly longer 6-32 machine screws. After that, tap four threaded holes at each end of each bar, for the 6-32 screws you will use to attach the square mounting plates of double-caster wheels.
You now have a case with (recommended) 2" to 2.5" dia. double caster wheels, and you have not done anything to "mod(ify)" your brand-new case. Put the rubber feet that came with it in a plastic bag, store them in your parts-locker, and call it a day.
You won't have any ventilation problems now, with your computer sitting in a carpeted area.