  Thermal evolution models suggest that the luminosities of both Uranus and
Neptune are inconsistent with the classical assumption of an adiabatic
interior. Such models commonly predict Uranus to be brighter and, recently,
Neptune to be fainter than observed. In this work, we investigate the influence
of a thermally conductive boundary layer on the evolution of Uranus- and
Neptune-like planets. This thermal boundary layer (TBL) is assumed to be
located deep in the planet, and be caused by a steep compositional gradient
between a H-He-dominated outer envelope and an ice-rich inner envelope. We
investigate the effect of TBL thickness, thermal conductivity, and the time of
TBL formation on the planet's cooling behaviour. The calculations were
performed with our recently developed tool based on the Henyey method for
stellar evolution. We make use of state-of-the-art equations of state for
hydrogen, helium, and water, as well as of thermal conductivity data for water
calculated via ab initio methods. We find that even a thin conductive layer of
a few kilometres has a significant influence on the planetary cooling. In our
models, Uranus' measured luminosity can only be reproduced if the planet has
been near equilibrium with the solar incident flux for an extended time. For
Neptune, we find a range of solutions with a near constant effective
temperature at layer thicknesses of 15 km or larger, similar to Uranus. In
addition, we find solutions for thin TBLs of few km and strongly enhanced
thermal conductivity. A $\sim$ 1$~$Gyr later onset of the TBL reduces the
present $\Delta T$ by an order of magnitude to only several 100 K. Our models
suggest that a TBL can significantly influence the present planetary luminosity
in both directions, making it appear either brighter or fainter than the
adiabatic case.
