The exact measurement of specific heats of substances with low thermal conductivity is connected with certain difficulties, since small heat flows in such substances lead to a relatively high temperature gradient; moreover the temperature exchange occurs rather slowly. Both influences are decisive, whatever method of measurement may be used. They require additional conditions, which must be noted and complied with, when dimensioning the calorimeter and selecting the experimental conditions. These problems are discussed in this article. In this connection a solution of the equation of thermal conductivity is given for the temperature field pattern in a hollow sphere with certain initial temperature distribution, while the sphere is heated with constant thermal power from inside and adiabatically isolated on the outside.