Context. Results from global magnetoconvection simulations of solar-like stars are at odds with observations in many respects: Simulations 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 nonaxisymmetric 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 to a semi-global spherical setup that describes the 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 nonaxisymmetric transition point is shifted towards higher rotation rates. We also find a change in the propagation direction of ADWs that means that prograde waves are also now found. However, the transition from an anti-solar to solar-like rotation profile is also shifted towards higher rotation rates, leaving the models in an even more unrealistic regime. Conclusions. Although 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 better match the observations.