A coupled plasma sheath/ablation model is developed for electrothermal chemical gun applications. By combining a commonly employed collisional sheath model with a previous ablation model, the convective heat flux as a function of time to the propellant bed is determined for two potential clectrothermal chemical gun propellants, XM39 and JA2. It is found that the convective heat flux varies smoothly from a nearly collisionless to a fully collisional regime over the short duration of the plasma pulse. The possibility of determining an accurate estimate of the amount of heat flux to the propellant bed due to radiation from the bulk plasma presents itself.