On the road toward experimental realization of laser-induced cooling of semiconductors, theoretical investigations are necessary for a detailed understanding of the microscopic phenomena underlying the cooling process, and for a prediction of optimal parameter regimes where efficient cooling could be expected. A recent realistic theory for cooling of bulk GaAs by Sheik-Bahae and Epstein has focused on the high-temperature regime, where the cooling process involves absorption of and luminescence from an electron-hole plasma. Using a microscopic many-particle theory, we extend the Sheik-Bahae Epstein approach to the low-temperature regime, where excitonic effects, i.e. effects of bound electron hole pairs in quasi-thermal equilibrium with correlated unbound pairs (i.e. the plasma) become important. We use a diagrammatic approach that is non-perturbative in the Coulomb interaction and contains effects of phase-space filling, single-particle renormalization in a partially ionized plasma, and screening. We ensure that our theory contains the relevant limiting cases for (partial) ionization in the low-density regime (Saha equation and Beth-Uhlenbeck formula) as well as the high density regime (Mott transition). Based on our microscopic theory for absorption and luminescence in the quasi-thermal equilibrium regime, we present a detailed study of cooling criteria at low temperature, focusing mainly on the temperature regime between 5K and 100K. In particular, we discuss the transition from the high temperature regime dominated by absorption in the e-h continuum to the low-temperature regime dominated by resonant exciton absorption.