It is true that soundproofing works by converting energy that is in
the form of noise into heat, however it's worth realising it's tiny.
Noise generators in a PC are fans & motors, usually motors if the
cooling paths are clear of obstruction immediate to fan blades.
Those fans & motors add up to 10W at most even on a large server,
most of that energy being emitted in the form of heat, not noise. The
noise energy is probably 10% of that at most or about 1W.
Thus soundproofing your case doesn't make it hotter, unless you
disrupt airflow or physically clog air inlet or outlet holes in the case.
The higher the wattage of your fans, and the greater the number,
the better it is usually to run them in extract mode. This is because
the fan dissipates heat according to the wattage marked on it, which
can be 1W, 2W or 5-7W for typical PC case fans. If you have 10 5W
fans on the inlet, you are pre-heating the air with 50W of heat. If the
fans conversely are on the outlet, that heating merely elevates air
that has already been extracted from the case, and is only then a
problem if the machine can materially increase surrounding ambient.
Conversely, fans run in extract-mode extract hotter air than they would
if used as intake fans - and the hotter the air, the shorter the life of the
bearings in the fan. This is where PSU fans should always be the best,
yet invariably aren't and thus most PSU failures are fan related.
So there are positives & negatives to either use.
Fan noise can be reduced in cases by 2 things:
o Insetting fans away from rear panels, and lining that short duct with
soundproofing material - both mass & acoustic foam (QuietPC 3-pk)
o Forcing outlet air to deviate 90-degrees, ideally 180-degrees
----- each 180-degree turn in airflow reduces noise by 6dB(A)
----- should also be realise it reduces airflow by introducing static pressure
Some cases, mainly very expensive Compaq servers have air holes in
strategic locations - so cool environment air is drawn in at these places
to reduce spot temperatures in the immediate area. Generally these are
obvious, as opposed to the hole-afterthought of some case designs