Wire mesh is a useful structural material for combustors, which has the thermal effect of quenching, holding or enhancing a flame. Previous researches mainly focused on the interaction between premixed flame and wire mesh in confined/semi-confined pipes, and the mesh, in addition to the thermal effect on flames, also induced a dynamic resistance to the flow in the pipes. This study aims to independently elucidate the thermal effect of a single-layer wire mesh insertion on the laminar coflow propane/air diffusion flames, wherein the dynamic effect of mesh is negligible. The wire mesh and flame properties were varied to investigate their effects on flame dynamics, including the mesh thermal conductivity, mesh porosity, mesh insertion positions above the burner, and fuel flow rates. The results show that flames could not pass through a mesh with high thermal conductivity, low porosity or low insertion position, and the mesh temperature, T m , measured in such cases was low. This suggests that the flame behavior is closely related to T m . The critical mesh temperature, T m , c r t , between flame passing and not passing through wire mesh in all tested cases was determined to be 965±15 K, i.e., flames can pass through a mesh only if T m > T m , c r t . An empirical method was proposed to estimate T m , which well matched the experimental data. Further, for all cases of flame passing through mesh, the flame height could be reduced using a mesh with high thermal conductivity or low porosity while maintaining the same flame speed, and a general formula was developed to describe the flame height. In summary, a single-layer wire mesh can function as a flame inhibitor or holder rather than an enhancer when “cutting” a buoyancy-driven diffusion flame.