Apparently, there is no change in metabolic rate if the fast is 72 hours or less, which means you keep burning body fast at your normal metabolic rate. The author of Leangains advises the following:
"A high meal frequency does not boost your metabolism, nor does fasting or a low frequency slow it down either. The latter has been shown quite clearly when researchers made people fast for 72 hours and found no difference in metabolic rate at the 12 hour mark, compared to the 72 hour mark. That's three days without food, yet all subjects retained a fully intact metabolic rate. There are other studies looking at one meal a day and alternate day fasting that does not find an impact on metabolism either.
Some studies have actually found that fasting boosts metabolic rate slightly during the initial 36 hours - this is supposedly an evolutionary response, mediated by norepinephrine, as the body mobilizes extra energy when food is scarce. You can imagine it would be highly counterproductive to mister caveman if he found himself slow and lethargic when he needed to find food in order to not starve to death."
The studies referenced in this excerpt:
Zauner C, Schneeweiss B, Kranz A, Madl C, Ratheiser K, Kramer L, Roth E, Schneider B, Lenz K. Resting energy expenditure in short-term starvation is increased as a result of an increase in serum norepinephrine. Am J Clin Nutr. 2000 Jun;71(6):1511-5.
Webber J, Macdonald IA. The cardiovascular, metabolic and hormonal changes accompanying acute starvation in men and women. British journal of nutrition 1994; 71:437-447.
And this post is interesting too if you fancy a long read:
http://www.leangains.com/2010/10/top-ten-fasting-myths-debunked.html?m=1