Due to the wide applicability of Cellular Automata (CA), as well as their inherent visual representation, the interest in methodological advances in CA simulation is growing. In the field of microstructure evolution, coupling CAs with concentration fields has been successfully achieved, thereby widening the applicability of CAs to diffusion-controlled transformations. Since vast cell domains are required for representative results for many complex microstructures, a computational bottleneck arises. This bottleneck can be effectively mitigated by embracing the Frontal Cellular Automata (FCA) paradigm. To date, published research on FCA-based models for diffusion-coupled microstructure evolution with grid independence and adaptive mesh coarsening is scarce. This work aims to develop an FCA framework for the simulation of diffusional phase transformations during the heating, annealing and cooling of cold-rolled steels. The large difference in carbon mobilities in ferrite and austenite is exploited to enable a straightforward formulation of carbon flow balances for ferrite interface cells as well for the overall ferrite phase. Since the carbon flow balances inherently contain all the interface coordinate information, there is no need for complex iterative schemes, allowing ferrite to adopt arbitrarily complex shapes. Describing several isolated ferrite grains as one ferrite instance with a "complex shape" enhances the stability of the simulation and effectively represents infinite ferrite-ferrite and ferrite-austenite grain boundary diffusion. Transition probabilities are calculated from the local carbon flow balances using Boltzmann principles and thermodynamic considerations based on the local chemical composition. The transition probabilities can be further modified using a consistent interpretation framework of the neighborhood based on Cahn-Hilliard calculations. This approach allows recovery, recrystallization, and other diffusion-independent mechanisms to be gradually incorporated into the simulation.