Recently, electric vertical takeoff and landing (eVTOL) aircraft have garnered significant interest as a primary mode of transportation in advanced air mobility (AAM). For the conceptual design of eVTOL aircraft, where a broad design space must be explored rapidly, a practical and reliable battery sizing process is essential. This process needs to employ models with low computational cost while comprehensively considering two key factors: voltage drop characteristics and thermal effects. However, existing research on battery sizing mainly relies on constant specific energy or power, neglecting these factors. This oversight can lead to significant discrepancies in battery sizing between the conceptual and detailed design phases. To address these limitations, this paper introduces a refined battery sizing process. Our approach incorporates models for battery voltage drop, heat generation, and a cooling system. A Thevenin equivalent circuit is used to model voltage drop and heat generation, with a novel calibration method developed for accurate predictions of voltage and temperature profiles. An air cooling system is adopted for its simplicity and lightweight design, and a corresponding model is constructed. Applying our process to eVTOL aircraft sizing revealed that incorporating temperature, along with the depth of discharge (DoD) and C-rate, as constraints in battery sizing led to a 4.6 % decrease in specific energy and a 4.2 % decrease in specific power. These findings underscore the importance of considering temperature in battery sizing. Additionally, sensitivity analyses provided insights into which thermal management system, air-cooled or liquid-cooled, is more appropriate for the battery under various operating conditions.