A number of recent experiments report on a correlation between the low-temperature slope of the thermopower, alpha/T, and the specific heat coefficient gamma=C_V/T for heavy fermions and valence fluctuating compounds with Ce, Eu, Yb, and U ions. Assuming that charge and heat currents at low temperatures are transported by quasiparticles, we first derive the universal value for the ratio q=alpha/(gamma T) using macroscopic transport equations. We then calculate the thermal response of the Fermi liquid (FL) regime of the periodic Anderson model and of the Falicov-Kimball model by dynamical mean field theory and find the q ratio. Eventually, we calculate the temperature dependence of alpha(T) above the FL regime using the "poor man's" approach, which describes the scattering of conduction electrons on the lattice of f ions by the single impurity Anderson model with crystal field (CF) splitting. The overall temperature dependence is obtained by interpolating between the FL and the poor man's solution, and is explained in simple terms. The shape of alpha(T) is determined by the relative magnitude of the Kondo scale T_K and the CF splitting. Pressure or doping (chemical pressure) affects alpha(T) by transforming the narrow Kondo resonances into a broad spectral function typical of valence fluctuators. This changes the effective degeneracy of the f state and results in a drastic modification of alpha(T). Temperature also changes the degeneracy of the f state by populating the excited CF states. Since T_K is strongly pressure dependent, while the CF splitting is not, the shape of alpha(T) is a sensitive function of pressure or doping. These results explain the near universality of the q ratio and the overall behavior of alpha(T) in EuCu₂(Ge_1-xSi_x)₂, CePt_1-xNi_x, YbIn_1-xAg_xCu₄, and similar systems.