  We investigate the location of the (unique) hot spot in a convex heat
conductor with unitary initial temperature and with boundary grounded at zero
temperature. We present two methods to locate the hot spot: the former is based
on ideas related to the Alexandrov-Bakelmann-Pucci maximum principle and
Monge-Amp\`ere equations; the latter relies on Alexandrov's reflection
principle. We then show how such a problem can be simplified in case the
conductor is a polyhedron. Finally, we present some numerical computations.
