The precise evaluation of real-world thermoelectric cooling (TEC) performance is vital for both the development of TEC devices, and for the rational design of TEC materials. Due to the relatively limited temperature difference (ΔT) that a single-stage TEC can achieve, the classical analytical formulae for thermoelectric cooling are commonly used with averaged material properties in the cooling performance evaluation. Nevertheless, this could cause remarkable errors in evaluations of the cooling power, even under a ΔT as low as 10 K. In this work, a cumulative model for thermoelectric cooling is proposed to evaluate the maximum coefficient of performance (COP) as well as the maximum cooling power of a TEC device under finite temperature differences, with the temperature dependence of material properties being fully considered. The inherent deficiencies in predicting the maximum cooling power by both the classical formulae and the original cumulative model are identified, and effective refinements are implemented to reduce the prediction error. Eight thermoelectric materials with state-of-the-art ZT values near room temperature are assessed for electronics cooling scenarios within a cold side temperature (T_c) range of 300-350 K. In comparison to the classical formulae, the proposed model predicts the maximum COP with comparably satisfying accuracies (±2%), while significantly improves the prediction accuracy of the maximum cooling power from approximately ±30% to within ±5% over a ΔT range of 10-70 K. This work fills the gap between thermoelectric material properties and device-level cooling performance, and is beneficial to the development and application of thermoelectric conversion technology for cooling purposes.