Presumably, you refer to this case:
http://www.mini-box.com/M350-universal- ... -enclosure
It does not look ideal for passive cooling, but rather, low airflow cooling. Convection will not cool enough w/o massive heatsink area, which is not feasible in such small case. But a samll amount of airflow is enough to drop temps by large margins for low power CPU/chipset.
Rethink. Consider low profile quiet fan coolers. If you want passive, go to a heatpipe-heatsink style case designed specifically for it --
http://www.silentpcreview.com/Coolermas ... i-ITX_case
ps -- if the system is running just one quiet fan, unless it vibrates a lot, there won't be a hum; that is most often caused by a HDD making the chassis vibrate (90 or 120Hz & harmonics)