Um.. it makes sense to me (that there would be a SLIGHT increase in heat for a SHORT period of time after its turned off, not enought to warrent a need for cooling though).
but as for the original question you could either:
Use a second PSU that is always on to power some of the fans.
Use a power adaper for somthing like a CD player (only more voltage), a 12v DC converter would run it at the same speed, a 4.5v (used in most 2 battery CD players) would run most decent fans and be almost silent.
Use one of these fancy pantsy gadgets.
Use some caps to run it for a pretty short ammount of time after the power is cut to the 12v rails.
I would use the adapter if I needed to do thise for some reason, however I don't seen why I would do this because it being hot wont make a differnce when the comptuer is off, eventually it WILL cool down to ambient wether there are fans in there or not, and how long it takes wont matter as long as, while its off (right after when it might heat up) it doesn't get hotter than like 70C, and it won't unless the fans go off. According to the graph which probably exagurates a bit the tempurature spikes for about 30 seconds before it starts dropping again and it only goes up by about 2C, probabl less than the differance btwn load and idle for most people.