  It is a long-lasting task to understand heat conduction phenomena beyond
Fourier. Besides the low-temperature experiments on extremely pure crystals, it
has turned out recently that heterogeneous materials with macro-scale size can
also show thermal effects that cannot be modelled by the Fourier equation. This
is called over-diffusive propagation, different from low-temperature
observations, and is found in numerous samples made from metal foam, rocks, and
composites. The measured temperature history is indeed similar to what
Fourier's law predicts but the usual evaluation cannot provide reliable thermal
parameters. This paper is a report on our experiments on several rock types,
each type having multiple samples with different thicknesses. We show that
size-dependent thermal behaviour can occur for both Fourier and non-Fourier
situations. Moreover, based on the present experimental data, we find an
empirical relation between the Fourier and non-Fourier parameters, which may be
helpful in later experiments to develop a more robust and reliable evaluation
procedure.
