Is a special intention required for the Basmala when performing Wudu', or is the intention for Wudu' sufficient, with the Basmala being a part of it?

The intention must be present at the first obligatory act of purification, and it is recommended to be present at the first of its sunnah acts. Wudu (ablution) is a single act of worship; its actions do not require a separate intention for each. The tasmiyah (saying "Bismillah") is one of the actions of wudu, and the intention for wudu suffices for it. So, if one intended purification and then lost awareness of that intention, a single intention is sufficient for him, as long as he did not intend cooling off or cleaning rather than purification.