We provide detailed background, theoretical and practical, on the specific heat of minerals and mixtures thereof, ‘astro-materials’, as well as background information on common minerals and other relevant solid substances found on the surfaces of solar system bodies. Furthermore, we demonstrate how to use specific heat and composition data for lunar samples and meteorites as well as a new database of endmember mineral heat capacities (the result of an extensive literature review) to construct reference models for the isobaric specific heat cp as a function of temperature for common solar system materials. Using a (generally linear) mixing model for the specific heat of minerals allows extrapolation of the available data to very low and very high temperatures, such that models cover the temperature range between 10 and 1000 K at least (and pressures from zero up to several kbars). We show how to calculate model specific heat as a function of temperature for a number of typical meteorite classes with known mineralogical compositions, for well-described laboratory regolith analogues, as well as for planetary ices and ‘tholins’ in the outer solar system. We describe a procedure to estimate cp(T) for virtually any solid solar system material with a known mineral composition. Part II will present and review of the heat capacity database for minerals and compounds and part III is going to cover applications and standard reference compositions and cp(T) curves and a comparison with new and literature experimental data.