Unsteady heat transfer processes between a heat source and the environment are completely described by the frequency-dependent heat transmission matrix within linear response theory. The 2×2 matrix characterizes the linear relation between the temperature and the heat transfer rate at the heat source and the environment sides of the system. In generic case, the heat transmission matrix has four independent complex entries. The number of independent elements may be reduced in the presence of certain properties or symmetries of the system. In the present paper, it is shown how the microscopic, governing equations influence whether the heat transmission matrix has a determinant of unity. A determinant fixed to one allows only three independent elements of the matrix. In the presence of a spatial symmetry under which the roles of the heat source and the environment are changed, the number of independent entries is reduced to two. The two independent elements may be formulated in terms of an effective thermal resistance and an effective heat capacity. In the case of a heat conducting wall, the effective values are independent of the frequency and equal to the static thermal resistance and heat capacity of the system. For generic symmetric systems, however, the effective thermal resistance and heat capacity may exhibit significant frequency dependence. The frequency dependence is numerically studied in the example of the heat conduction between two parallel pipes.