Should the Basmalah be written for one who says it to himself before ablution, and what is the difference between that and the thoughts for which a person is not held accountable?

Uttering "Bismillah" (in the name of Allah) to oneself is considered a form of remembrance by the heart, which is permissible and rewarded. Uttering "Bismillah" is obligatory for ablution according to some scholars, and sunnah (recommended) according to the majority. Uttering "Bismillah" is achieved by pronouncing it audibly enough for the person performing ablution to hear it, or by moving one's tongue and lips. As for fleeting thoughts and whispers, they are from Satan and are not held against a person unless acted upon or spoken aloud, because they occur without the person's choice and are often contrary to the Sharia.