  This study focuses on thermal superpotentials in asymptotically anti-de
Sitter spacetimes. We study the thermal superpotential and its use as a
counterterm for the renormalization of the gravitational action in designer AdS
theories with a self-interacting scalar field. Our findings, which are
consistent with prior works, demonstrate that, for the thermal superpotential
to be a suitable counterterm, it must have some specific form.
