Positron tomography was used to investigate modulations of brain activity during the so-called resting state that may occur due to a concurrent cognitive training. Twelve subjects were repeatedly scanned during resting periods and while solving logical problems containing a bias causing them to make reasoning errors. At experiment mid-time, eight subjects were trained to inhibit the reasoning bias so that their performance in solving logical problems dramatically increased afterwards, while the other four subjects were trained to logical reasoning only which did not help improving their performance. In the subgroup of subjects who increased their performance after training, we found that during the post-training resting periods, as compared to pre-training resting periods, brain activity increases in areas not belonging to the classical resting network, namely the midbrain, thalamus, peristriate, inferior frontal, and ventromedial prefrontal cortices. Strikingly, in this subgroup of subjects, these same areas were found to be also more active during post-training successful execution of the logical task, as compared to pre-training erroneous execution of the task. Such findings were not observed in the subgroup of subjects who did not improve their performance after training to logic only. These results indicate that the brain default mode is a dynamic state during which context dependent local increases of cerebral blood flow may occur on a short-term, likely for the consolidation of newly acquired knowledge.