A self-ignition of a deuterium-deuterium (D-D)-3He fuel field-reversed configuration (FRC) plasma by fusion product heating is studied by using the point plasma model, where an FRC plasma equilibrium is taken into account. It is numerically demonstrated that the D-D-3He plasma can be evolved from a deuterium-tritium burning plasma in a controlled manner by means of a compression-decompression control as well as a fueling control. It is also indicated that the increase of a trapped flux is effective for suppressing the excessive elongation of a plasma during the transition. The proposed method may provide a solution to the problem on plasma heating to attain a D-D-3He self-ignition.