New studies are emerging to reduce energy costs and become a more sustainable society. One of the processes where the greatest savings can be made is in cooking, due to its large-scale global use. In this vein, this study aims to analyse the influence of the vessel in the thermal efficiency at the cooking process. For that purpose, a numerical model of a cooking vessel was designed and validated with three different experimental heating tests. One of the key factors of the process is the contact between the vessel and the glass, therefore, two new approaches to model the thermal contact between the vessel and the cooktop were explored. Once the numerical models were calibrated, a full factorial analysis was performed to quantify the influence of the key parameters of the vessel in the heating process during cooking (thermal conductivity, specific heat, convection and radiation coefficients, and vessel concavity). Two of the most influential parameters in the heating process are the conductivity and the thermal contact between the vessel and the glass. Higher cooking efficiency can be achieved both with a low thermal conductivity vessel and with a high concavity, i.e., increasing the isolation between the vessel and the glass.