It is very important for reactor design and control to choose and control the temperature throughout the reaction process. The linear stability analysis showed that control parameters contained in a nonlinear kinetic system of equations resulted in the diversity of temperature self-organization structures and occurring critical values in Lindemann uni-molecular chemical reaction-diffusion-heat conduction systems. The results of numerical simulations also showed that the differences of occurring critical values of Turing bifurcation led to multiple wave number values of spatially periodic structures of temperature field. Without doubt，these significant results should be considered in order to reasonably design，correctly choose the reactor type and optimally control chemical reactors.