A numerical study has been undertaken to predict quantitatively each of the non-isothermal reaction modes (stationary-state reaction, oscillatory cool flames and oscillatory two-stage and multiple-stage ignitions) associated with the oxidation of ethanal in a non-adiabatic well-stirred flow system (0.5 dm$^3$) at a mean residence time of 3 s. The kinetic scheme comprises 28 species involved in 60 reactions and it is coupled to the thermal characteristics through enthalpy change in each step, heat capacities of the major components and a heat transfer coefficient appropriate to heat loss through the reaction vessel wall. Spatial uniformity of temperature and concentrations is assumed, matching the experimental conditions. Very satisfactory accord is obtained between the experimentally measured and predicted location of the different reaction modes in the (p-T$_a$) ignition diagram (where p is pressure and T$_a$ is temperature at ambient conditions), and the time-dependent patterns for oscillatory reaction agree with experimental measurements. The competition between degenerate branching and non-branching reaction modes is governed ultimately by the equilibrium $CH_3 + O_2 \leftrightharpoons CH_3O_2.$ The predicted behaviour is found also to be especially sensitive to the rate of decomposition of the acetyl radical $CH_3CO + M \longrightarrow CH_3 + CO + M.$ Corrections for its pressure dependence are essential if the predicted form of the oscillatory cool flame region in the (p-T$_a$) diagram is to match the experimental results. Variations of the rate of this reaction also give new kinetic insight into the origins of complex oscillatory wave-forms for cool flames that have been observed experimentally. Relationships between the results of the detailed kinetic computations and the predictions from a three-variable, thermokinetic model are examined. This model is the simplest of all reduced schemes that makes successful predictions of two-stage ignition phenomena.