It helps these computers didn't use much power, probably didn't even have much of a heatsink on the CPU. Someone in this thread quoted 3 watts for the CPU. Of course with this many of them you might be using something like a kilowatt (for all the components) which is enough to make a room quite warm, but not damaging. Think about a kilowatt space heater - it's not really dangerous to things that don't directly touch it.

If it's like the old ISPs I was familiar with, they didn't. The POP (point-of-presence, 100's of modems, plus several terminal servers, routers, etc.) would generally be in some basement without any cooling at all. There would literally be warped plastic.