The heat transfer by simultaneous conduction, convection and radiation between flame and fuel surface in a thermally radiating medium is investigated theoretically. The flame and fuel surface are assumed to be the boundaries of diffuse, non-black, infinite, isothermal, parallel surfaces separated by a finite distance. The space between the plates is supposed to be filled with a radiatively absorbing, emitting, scattering medium. The problem is formulated exactly in terms of simultaneous integrodifferential equations. The numerical results reveal the effect of the system parameters on the heat transfer characteristics and the temperature distributions.