"SLEEP GOOD . . . FIRE BAD" - Frankenstein
This topic is pretty well documented at an anecdotal level in sleep deprivation, but here's the story of a single study done in 1989 on total sleep deprivation in rats. (Those of you that love animals may want to skip this one - it doesn't have a very happy ending.):
This is the setup: A rat is placed into a circular testing chamber and confined to one half by a vertical partition. The partition is motorized so that it can rotate about the center axis of the room; this forces the rat to move about when the partition is in motion. EEG sensors attached to the animal monitor wakefulness, and when sleep onset is detected, the partition is automatically set into motion, forcing the rat to wake up and walk about. In this way, the rat is not allowed to sleep more than a few seconds at a time. Food and water provided ad-lib.
What happens? The rat *dies* in 10-20 days. Some rats in this study were selected to be taken out of the chamber and allowed to sleep ad-lib for the rest of the experiment: rats taken out before 10 days did pretty well; rats taken out after 10-15 days usually died as well.
Why did they die? The researchers noticed that before the animals died, they developed skin lesions and lost weight despite doubling their food intake. Further investigation showed that the animals died from hypothermia even though on average they ate twice the normal amount of food, experienced increased heart rate and respiration, increased blood epinephrine levels and a 250% increase in metabolic rate. Other studies suggested that the metabolic rate increase in total sleep deprivation is so drastic that the body resorts to digesting the protein of its own muscles (hence the skin lesions.)
In other words, the animals died from excessive heat loss, even though their internal thermostats were turned up to "deep fry."
This answer is slightly paradoxical - (if the rats were indeed metabolizing more food, all of that chemical energy had to go somewhere!) The most plausible explanation is that the mechanisms that control sleep are intimately coupled to body thermoregulation mechanisms (some theories suggest that sleep is an evolutionarily advantageous way to conserve body energy/food, see Sleep: The metanode), and that total sleep deprivation seriously disrupts a body's ability to thermoregulate properly.
What does this mean for humans? Well, the news is good: First, since humans have such a high body mass to surface area ratio, it could take 2-6 months of total sleep deprivation to kill you. Also, it seems that sleep control mechanisms in differ between humans and rodents, so a person might very well survive total sleep deprivation, though I wouldn't want to be the one to find that out. Finally, the animals in the above study were under extraordinary stress, which may have contributed to their quick demise. Since I've never known ANYbody to be under stress while sleep deprived, we can't predict exactly how humans would respond.
The original experiment described can be found in the article "Sleep deprivation in the rat III, Total sleep deprivation" in the journal Sleep Volume 12, pp 12-31, 1989