The influence of oxygen enrichment of the air co-jet on the combustion of a laminar methane jet diffusion flame is studied experimentally by the measurement of the heat flux transferred to an assembly of heat exchangers with oxygen concentration ranging from 21% to 41% and firing rates ranging from 0.5 to 1.2 kW. It is observed that, as expected, heat flux increases with oxygen concentration; less methane is necessary to produce the same heating effect as oxygen index is increased. The radiant fraction is found to increase with the oxygen concentration. Deducing the convection part, it is shown that convection is highly dependent on the flame regime with a lesser rate of increase when the flame is reattached to the burner. Evolution of the convective coefficient may be used as a detection of the transition from a lifted flame to a flame attached to the burner.