The proposition of hyperbolic conduction (also known as the second sound wave) for materials with non-homogeneous inner structure has run into a serious controversy in recent times. While one group of investigators has observed very strong evidence of hyperbolic nature of conduction in such materials and experimentally determined the corresponding relaxation times to be of the order of tens of seconds, the other group proclaims that their experiments do not show any such relaxation behaviour and the conventional Fourier law of conduction is good enough to describe conduction in them. This paper is an effort towards resolving this controversy. In the first place the experimental philosophies and techniques of both the groups have been thoroughly examined. It has been observed that determination of thermophysical properties independent of the relaxation time measurement is an inherent inconsistency in all these experiments. Additionally the assumptions regarding temperature input might have also played a role to arrive at diverging conclusions. Based on these observations an experimental method has been suggested in this study which uses temperature oscillation in semi infinite medium to determine the thermal diffusivity and the relaxation time simultaneously from a single experiment. Using this technique the wide range of experiments conducted reveal that there exists a definite hyperbolic effect in the "bulk" conduction behaviour of such materials although it is somewhat less in extent to those reported by investigators claiming existence of hyperbolic conduction. Also a wide range of experiments with variation of parameters such as packing material, its particle size, filling gas used and its pressure and temperature have been conducted. The data presented here for the wide range of parameters can be useful for further investigations and plausible explanation of "bulk conduction" in materials with non-homogeneous inner structure.