  Context. The dynamics of a low-mass protoplanet accreting solids is
influenced by the heating torque, which was found to suppress inward migration
in protoplanetary disks with constant opacities.
  Aims. We investigate the differences of the heating torque between disks with
constant and temperature-dependent opacities.
  Methods. Interactions of a super-Earth-sized protoplanet with the gas disk
are explored using 3D radiation hydrodynamic simulations.
  Results. Accretion heating of the protoplanet creates a hot underdense region
in the surrounding gas, leading to misalignment of the local density and
pressure gradients. As a result, the 3D gas flow is perturbed and some of the
streamlines form a retrograde spiral rising above the protoplanet. In the
constant-opacity disk, the perturbed flow reaches a steady state and the
underdense gas responsible for the heating torque remains distributed in
accordance with previous studies. If the opacity is non-uniform, however, the
differences in the disk structure can lead to more vigorous streamline
distortion and eventually to a flow instability. The underdense gas develops a
one-sided asymmetry which circulates around the protoplanet in a retrograde
fashion. The heating torque thus strongly oscillates in time and does not on
average counteract inward migration.
  Conclusions. The torque variations make the radial drift of the protoplanet
oscillatory, consisting of short intervals of alternating rapid inward and
outward migration. We speculate that transitions between the positive and
oscillatory heating torque may occur in specific disk regions susceptible to
vertical convection, resulting in the convergent migration of multiple
planetary embryos.
