A dynamical theory for two-photon autocorrelation functions (AF) which takes into account interaction of a chromophore with phonons and with huge number of tunneling systems (TSs) of a cooled polymer is developed. The interaction with one extrinsic TS, which relates to the chromophore with its nearest environment and has undergone light-induced tunneling, and the interaction with a huge number of intrinsic TSs inherent in a polymer, which have undergone spontaneous tunneling, is considered. Relaxation of these TSs results in both exponential and logarithmic spectral diffusion. Both types of spectral diffusion manifest themselves in AF. Influence of temperature on AF is studied. Experimental data for AF in low temperature polymers are treated on the basis of our theory.