A simple idea is proposed to produce an excess enthalpy flame by inserting a porous solid of high thermal conductivity into the one-dimensional flame zone. Heat is recirculated internally through the solid from the downstream high temperature region to the upstream low temperature region and large excess enthalpy is produced at the head of the reaction zone. The potentiality of the proposed artificially modified flame is analyzed on the basis of the simplified one-dimensional flame theory. It is found that in this flame the mass flow rate is not the eigenvalue but becomes a mere parameter. The heat transfer coefficient between the solid and the reacting gas is another parameter. With these additional two parameters the controllability over the flame characteristics increases remarkably. The analysis reveals several attractive characteristics of the flame and that the proposed idea is promising to burn mixtures of low heat content in a simple combustion system.