  The motivation for this theoretical paper comes from recent experiments of a
heat transfer system of two thermally coupled rings rotating in opposite
directions with equal angular velocities that present anti-parity-time (APT)
symmetry. The theoretical model predicted a rest-to-motion temperature
distribution phase transition during the symmetry breaking for a particular
rotation speed. In this work we show that the system exhibits a parity-time
($\mathcal{PT}$) phase transition at the exceptional point in which eigenvalues
and eigenvectors of the corresponding non-Hermitian Hamiltonian coalesce. We
analytically solve the heat diffusive system at the exceptional point and show
that one can pass through the phase transition that separates the unbroken and
broken phases by changing the radii of the rings. In the case of unbroken
$\mathcal{PT}$ symmetry the temperature profiles exhibit damped Rabi
oscillations at the exceptional point. Our results unveils the behavior of the
system at the exceptional point in heat diffusive systems.
