Theoretical equations of critical thermal explosion and runaway in a non-isothermal reactor without chemical consumption were derived. The critical ignition, extinction and transition temperatures, modified Semenov＇s number and the stable criteria of temperature in reaction system can be estimated employing these equations. In an unsteady state reaction system the equations of critical modified Semenov＇s number and runaway temperature equations were also derived. The transient conversion and temperature profiles in the case of chemical consumption are the function of reaction time, which can be calculated numerically from two heterogeneous first order ordinary differential equations. Four parameters, i.e. n, beta, phi, and phi, affect those calculated results.