  We consider in this paper a perturbation of the standard semilinear heat
equation by a term involving the space derivative and a non-local term. In some
earlier work (Abdelhedi-Zaag JDE 2021), we constructed a blow-up solution for
that equation, and showed that it blows up (at least) at the origin. We also
derived the so called "intermediate blow-up profile". In this paper, we prove
the single point blow-up property and determine the final blow-up profile.
