During aluminium electrolysis, a ledge of frozen electrolytes is generally formed, attached to the sides of the cells. This ledge acts as a protective layer, preventing erosion and chemical attacks of both the electrolyte melt and the liquid aluminium on the side wall materials. The control of the sideledge thickness is thus essential in ensuring a reasonable lifetime for the cells. The key property for modelling and predicting the sideledge thickness as a function of temperature and electrolyte composition is the thermal conductivity. Unfortunately, almost no data is available on the thermal conductivity of the sideledge. The aim of this work is to alleviate this lack of data. For seven different samples of sideledge microstructures, recovered from post-mortem industrial electrolysis cells, the thermal diffusivity, the density, and the phase compositions were measured in the temperature range of 423 K to 873 K. The thermal diffusivity was measured with a laser flash technique and the average phase compositions by X-ray diffraction analysis. The thermal conductivity of the sideledge is deduced from the present experimental thermal diffusivity and density, and the thermodynamically assessed heat capacity. In addition to the present experimental work, a theoretical model for the prediction of the effective thermal transport properties of the sideledge microstructure is also proposed. The proposed model considers an equivalent microstructure and depends on phase fractions, porosity, and temperature. The strength of the model lies in the fact that only a few key physical properties are required for its parametrization and they can be predicted with a good accuracy via first principles calculations. It is shown that the theoretical predictions are in a good agreement with the present experimental measurements.