The degradation of aerodynamic performance due to ice accumulation on the airfoil remains a major risk in the current aviation industry. Although the Thermal Ice Protection System (IPS) is being increasingly used, remaining liquid water that is not fully evaporated can still flow and refreeze as runback ice. IPS design depends on accurate prediction of these ice shapes, but conventional high-fidelity numerical simulations, which combine fluid flow, heat transfer, and phase-change physics, are computationally demanding and often requiring several computing hours per configuration. Previous studies have applied reduced order and neural network models to predict ice accretion on unprotected airfoils showing good capability in capturing complex ice geometries. However, these works do not address ice accretion on thermally protected surfaces. This work presents a Surrogate Model-based using Neural Network Approach to mitigate the high computational demanding solver, which provides near-instantaneous prediction of surface temperature distributions and run-back ice formation on thermally protected airfoils. The model aims to facilitate uncertainty quantification (UQ) studies that are otherwise computationally intensive. The methodology uses supervised learning on the dataset, which was obtained by the solver in SU2 coupled with Lagrangian particle-tracking code, tracking the dispersed phase of liquid droplets, and the ice accretion solver PoliMIce, which tracks the phase change. A surrogate model is trained on a neural network via supervised learning to map key input parameters, i.e., Median Volume Diameter (MVD), Liquid Water Content (LWC), and freestream temperature (SAT), to output parameters, surface temperature profiles, and ice thickness along the surface. Preliminary results demonstrate that a surrogate model with surface temperature predictions yields an average R2 value of 0.95 across 3 different datasets and ice thickness geometries closely matching reference solutions. Computational time is reduced by approximately 97% compared to traditional solvers