Crystallization of polymers is composed of two processes, nucleation (birth) and subsequent growth of crystallites, which are in general both stochastic in time and space. If we assume that at points of contact between two growing crystallites they stop growing, a random division of the relevant region in a d-dimensional space is obtained, known as a random Johnson-Mehl tessellation, which has been studied in previous literature with homogeneous parameters. The coupling of the kinetic parameters of the birth-and-growth process with the underlying temperature field induces time and space heterogeneities (and stochastically) of all parameters involved, thus motivating a more general analysis of the stochastic geometry of the crystallization process. A complete charaterization of the final spatial structure of the crystallization (tessellation) can be given in terms of the mean densities of interfaces (n-facets: cells, faces, edges, verteces) of the random tessellation, at all different Hausdorff dimensions, with respect to the usual d-dimensional Lebesgue measure. Here an analysis of the above quantities in terms of the kinetic parameters of the process is presented coupled with the evolution equations of the underlying temperature field.