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Extensive research has been conducted on the use of the Cone Calorimeter to obtain flammability properties of materials for modeling. Ignition properties such as surface temperature at ignition (Tig) and thermal inertia (kρc) are typically determined on the basis of piloted ignition times measured at different heat flux levels. A specific functional relationship between piloted ignition time and heat flux is used to correlate the data and estimate the material properties. The functional relationship is based on the solution of a simplified form of the heat conduction problem in the Cone Calorimeter. Previous ignition studies have always assumed that the surface heat losses involve Newtonian cooling, which is characterized by a constant convection coefficient. However, earlier measurements obtained by the author show that the convection coefficient in the Cone Calorimeter for specimens in the vertical orientation could be more appropriately expressed as a quadratic function of the heat flux. This paper presents the experimental data and analysis that resulted in this proposed quadratic relationship. The solution of the modified conduction model is derived, and its use for the analysis of ignition data is illustrated for six solid wood species.