To establish the design principles of thermal properties of solids, we performed comprehensive calculations of volume thermal expansion coefficients α V , bulk moduli B T , average atomic volumes V, and Gruneisen parameters γ in the finite temperature for the 46 elements and 45 binary oxides using first-principles lattice-dynamics calculations. We clarified that (i) a crystal possessing large V tends to have small B T ; (ii) the major role of γ is the determination of the sign of α V , the value of which is ruled by the crystal structures and coordination numbers; (iii) the transverse-acoustic (TA) and/ or low-frequency phonons are responsible for the negative thermal expansion (NTE) behaviors; (iv) the NTE materials prefer the relatively large V with the void space, possessing negative mode-Gruneisen parameters γ qν ; and (v) the common feature of the NTE materials is the phonons vibrating forward to the void space. Our study provides a wide perspective on designing low and/or negative thermal expansion materials.