Quantum mechanical calculations, coupled with statistical thermodynamics, provide a means to obtain thermodynamic properties of ideal gas. In this work, we performed density functional theory (DFT) and statistical thermodynamic calculations of ideal-gas heat capacities and entropies for a set of 93 rigid molecules, which do not contain large amplitude motions, such as internal rotations or ring puckering, and for which reliable reference data were found in the literature. The effect of the size of basis sets and scale factors was systematically examined and statistically evaluated. The absolute average percentage deviations of the heat capacities and entropies calculated using unscaled harmonic frequencies from reference values were less than 2.5% for all of the basis sets studied. Both heat capacities and entropies were, however, systematically underestimated, and the relative deviations of heat capacities showed a significant temperature dependence with a maximum deviation near ambient temperatures. Scaling the calculated frequencies by a single value of scale factor from the literature led to slightly more accurate results, but the relative deviations remained biased (values were systematically overestimated) and significantly temperature-dependent. We propose a new wavenumber and bond-dependent set of scale factors that significantly improves the agreement between the theory and the reference data and provides an unbiased distribution of the relative deviations and a temperature dependence of the ideal-gas heat capacities which is closer to the reference data.