Biocatalytic reaction is a type of reaction which uses enzyme or whole-cell as a (bio)-catalyst to achieve a desired conversion, under controlled conditions in a bioreactor. Temperature produces opposed effects on enzyme activity and stability, and is therefore a key variable in any biocatalytic processes. An exothermic biocatalytic reaction, in a continuous-stirred-tank reactor (CSTR), was analyzed where dynamic equations (non-linear differential equations) could be derived from the Michaelis-Menten and Arrhenius equations, by performing mass and energy balances on the reactor. In this work, the effects of the different parameters such as dilution rate, proportional control constant and dimensionless total enzyme concentration, on the stability of the system, were studied. The stability of the reaction could be analyzed, based on the ODE (ordinary differential equation), solved using the numerical technique in MATLAB® and the analytical investigation using Mathematica.® The numerical analysis can be carried out by considering the hase-plane behaviour and bifurcation diagrams of the dynamic equations, while the analytical analysis using Mathematica® can be undertaken by evaluating the eigenvalues of the system. In order to model the operational stability of biocatalysts, modulation factors need to be considered so that a proper design of bioreactors can be done. Temperature, as a key variable in such bioprocess systems, can be conveniently optimized through the use of appropriate models.