The spatio-temporal temperature and species concentration distributions associated with low and intermediate temperature hydrocarbon oxidation are computed using a global thermokinetic scheme augmented with diffusive transport. The scheme used for the computations was proposed by Wang and Mou and is extended to include diffusion of species and heat. The conservation equations for species and energy are then derived and solved for a one-dimensional and an axisymmetric, spherical domain for temperatures ranging from 540 to 660K at subatmospheric pressures. The predictions are then used to develop ignition diagrams for different Lewis (Le) numbers. Increasing Le is found to promote oscillatory cool flames and two-stage ignition in the one-dimensional model, while the ratio of the mass diffusivity of the parent fuel to that associated with the autocatalytic chain carrier has a negligible effect on the structure of the ignition diagrams. In the spherical model, oscillatory cool flames and two-stage ignition were also predicted albeit at lower values of the Le.