The study is aimed at demonstrating a methodology for the time-scale characterization of the chemistry-wall-heat-transfer interaction. The driving chemical time-scale is estimated by means of the tangential stretching rate, and a proper thermal timescale for the temperature-time variation due to wall heat flux is presented. A thermal Damköhler number, Dath, is proposed as the ratio of the two. The methodology is applied on a prototypical laminar methane-oxygen diffusion flame impinging on an isothermal cold wall. Non-adiabatic effects are described qualitatively and a CSP-TSR analysis is performed to obtain topological information and physical insights. The thermal Damköhler number field is computed and discussed to highlight the interplay between chemical and diffusive processes and to a-priori assess the accuracy of the steady laminar flamelet assumption under non-adiabatic conditions.