  Context. Results from global magnetoconvection simulations of solar-like
stars are at odds with observations in many respects: They show a surplus of
energy in the kinetic power spectrum at large scales, anti-solar differential
rotation profiles, with accelerated poles and a slow equator, for the solar
rotation rate, and a transition from axi- to non-axisymmetric dynamos at a much
lower rotation rate than what is observed. Even though the simulations
reproduce the observed active longitudes in fast rotators, their motion in the
rotational frame (the so-called azimuthal dynamo wave, ADW) is retrograde, in
contrast to the prevalent prograde motion in observations. Aims. We study the
effect of a more realistic treatment of heat conductivity in alleviating the
discrepancies between observations and simulations. Methods. We use
physically-motivated heat conduction, by applying Kramers opacity law, on a
semi-global spherical setup describing convective envelopes of solar-like
stars, instead of a prescribed heat conduction profile from mixing-length
arguments. Results. We find that some aspects of the results now better
correspond to observations: The axi- to non-axisymmetric transition point is
shifted towards higher rotation rates. We also find a change in the propagation
direction of ADWs so that also prograde waves are now found. The transition
from anti-solar to solar-like rotation profile, however, is also shifted
towards higher rotation rates, leaving the models into an even more unrealistic
regime. Conclusions. Although a Kramers-based heat conduction does not help in
reproducing the solar rotation profile, it does help in the faster rotation
regime, where the dynamo solutions now match better with observations.
