DIY Hadoop Cluster - Heat & Dust issues?

Use real server cases with good cooling/ventilation paths.

Here's what I'd do.

Get some large sheets of thin Lexan (or even foam board / corrugated plastic board - I know this as Correx, YMMV).

Punch some holes through it, and bolt it to the holes on the uprights. Build about a foot or more higher on the top, cut out a hole and then mount a 12v automotive radiator fan on the top. You'll also want to build in some air-path through the "rack". One way to encourage airflow up and across would be to block alternate shelf-sides, and then build out a "box channel" for it to flow through. Side view.

                           || Fan Out
            | +-+--------->++          |
   And Up   | ||                       |
            | ||                       |
            | ||-----------------------+
            | ||                       |
            | |<----------------------+|
            | <--+                    ||
               | +--------------------+-+ |
               |                       || |
               |                       || |
               +-----------------------|| |Air flows up
               |       +----------------> |
               |   +-----------+       || |
               |   |           |       |+ |
               +---|Filter IN  |-------+--+
               |   |           |       |
               |   +-----------+       |

Cut out a panel at the bottom, and mount in that hole a filter from a ducted AC unit..

The theory is that air will be drawn up from the bottom (where it's cooler), through the filter panel, up past the servers, and out the hole with the fan in, on the top.

Or just buy a few 2U rack server cases from somewhere like Xcase, and then get a second hand rack to put them in.

Honestly? Unless its in a very dirty or very hot place (ambient temperature of above 30c in the room), nothing.

Those computers aren't going to generate much heat and there is loads of room around them to dissipate the heat they do generate. Not nearly enough to worry about in any case.