Heat and electronics don't mix. Never have. But the first time it was an obvious problem in the computer industry was when the 486DX processor was released in the early 1990s. They were significantly faster and hotter than the 486SX, and there were widespread problems. And it’s been a battle ever since.
With the January 2009 heatwave in South Australia and Victoria, computer equipment is under stress. Computers in an air-conditioned office will most likely function fine, but with temperatures still in the 30s overnight, once the aircon is off, computers left on will warm up very quickly and may crash, freeze or even fail outright.
If you have computers which need to remain on overnight, such as 24x7 web or e-commerce servers, you'll need to keep them air-conditioned. Otherwise, shutting everything off overnight, even the 8x5 line-of-business servers, is the best approach. In the morning, let the office cool off from the overnight heat before powering them back on.
Other devices which should be switched off include routers, hubs/switches, fax machines, printers and photocopiers. Some of these may slip into a low-power or sleep mode, and therefore cool off by themselves, but problems from blackouts may cause problems anyway, and being turned off is safest.