In this article, we investigate the impact of heat transfer between the flame and the flameholder on the dynamic stability characteristics of a 50-kW backward-facing step combustor. We conducted a series of tests where two backward step blocks were used, made of ceramic and stainless steel, whose thermal conductivities are 1.06 and 12 W/m/K, respectively. Stability characteristics of the two flame-holder materials were examined using measurements of the dynamic pressure and flame chemiluminescence over a range of operating conditions. Results show that with the ceramic flameholder, the onset of instability is significantly delayed in time and, for certain operating conditions, disappears altogether, whereas with the higher conductivity material, the combustor becomes increasingly unstable over a range of operating conditions. We explain these trends using the heat flux through the flameholder and the change in the burning velocity near the step wall. Results suggest a potential approach using low-thermal-conductivity material near the flame-holder as passive dynamics suppression methods. Copyright © Taylor & Francis Group, LLC.