Kurzban on that:

Clarke and Sokoloff remarked way back in the nineties that a “fashionable” view “equates concentrated mental effort with mental work,” but that “there appears to be no increased energy utilization by the brain during such pro-cesses.”52 A more recent review concluded that it is “unlikely that the blood glucose changes observed during and after a difficult cognitive task are due to increased brain glucose uptake.”53

Now, I'm not an expert on the brain's consumption of glucose, but you don't actually have to be an expert physiologist to notice something is amiss. Subjects in this literature who do a few minutes of a “self-control task” are referred to as “depleted.” What, precisely, is missing? Consider that in the radish/cookie experiment, subjects’ brains in both conditions have very similar sets of modules that are active. Basically, everything brains normally do is still going on—the senses, memory, monitoring autonomic activity, and so on. In the radish condition, some modules are, presumably, inhibiting others from causing the subject to indulge in the cookies. I don't really know if it is possible to estimate what fraction of modules differ between these two conditions. My guess is that this number would be small. Could these extra modules be draining the brain of glucose?

Consider that the entire brain uses about .25 calories per minute.54 If we suppose that the “self-control” task increases overall brain metabolism by 10%—a very large estimate55—then the brains of subjects who do one of these tasks for five minutes, who are categorized as “depleted,” have consumed an extra 0.125 calories. Does it seem right that you need 100 calories from lemonade to compensate for a tenth of a Tic Tac?56 Even worse for the glucose model, performance on “self-control” tasks should be much lower after exercise, which consumes orders of magnitude more glucose. However, research in this area shows exactly the reverse.57

Footnotes:

52 Clarke & Sokoloff 1998, p. 673.

53 Messier 2004, p. 39.

54 Clarke & Sokoloff 1998, p. 660.

55 I have in mind here evidence from imaging (PET, fMRI), in which percentage changes are small, and of course restricted to particular regions. See, e.g., Madsen et al. 1995.

56 Note also that in this work, researchers use Splenda for the control. While sucralose, which gives rise to the sensation of sweetness, is itself not metabolized, Splenda packets contain carbohydrates in the medium in which sucralose is delivered, and so have about 3 calories. The “zero calorie control” in these studies has an order of magnitude more calories than this (very large over-) estimate of how many calories are consumed. Note also that performance on physically taxing tasks (riding a stationary cycle) can be improved by simply swishing a sugar solution around in one's mouth (Chambers, Bridge, & Jones 2009). It could be that concentrated sugar in the mouth acts activates reward systems, which would explain why lemonade has this effect.

57 See, for example, Tomporowski 2003.

Cited references:

Chambers E. S., Bridge, M. W., & Jones, D. A. (2009). Carbohydrate sensing in the human mouth: effects on exercise performance and brain activity. Journal of Physiology, 587, 1779–1794.

Clarke, D. D., & Sokoloff, L. (1998). Circulation and energy metabolism of the brain. In G. Siegel, B. Agranoff, R. Albers, S. Fisher, & M. Uhler (eds.), Basic neurochemistry: Molecular, cellular, and medical aspects (6th ed.) (pp. 637–669). Philadelphia, PA: Lippincott-Raven.

Madsen P. L., Hasselbalch, S. G., Hagemann, L. P., Olsen, K. S., Bulow, J., Holm, S., Wildschiødtz, G., Paulson, O. B., & Lassen, N. A. (1995). Persistent resetting of the cerebral oxygen/glucose uptake ratio by brain activation: Evidence obtained with the Kety-Schmidt technique. Journal of Cerebral Blood Flow and Metabolism, 15,485–491.

Messier, C. (2004). Glucose improvement of memory: A review. European Journal of Pharmacology, 490, 33–57.

Tomporowski, P. D. (2003). Effects of acute bouts of exercise on cognition. Acta Psychologica, 112, 297–324.