Arendt has a scientific account for the soul rather than the classical transcendental view.  She brings the soul back to the here and now and lets it account for things like emotions and other parts of the 'inner life'.  This is important when discussing thought and the banality of evil because the soul is what connects the mind and the body.  If thoughtlessness is the cause of evil, then the link between the soul and the mind could be the key to how the person becomes thoughtless.  It also might be explained by the link between thought and speech.  If the 'evil-doers' were not thinking about what they were doing, then they wouldn't try to speak out against it or refuse to do his/her duties.  Regardless, the links Arendt draws in the first few chapters of her book, help to set the stage for the link between thoughtlessness and evil.