As the electrical grid evolves into a smart grid, efficient routing of power through transmission lines becomes essential to meet power demands. Real-time computations of line temperature and line current become important for dynamically rating transmission lines. This process becomes challenging as the transmission line system consists of complex electrical and thermal dynamics, which exist simultaneously and interact with each other. This makes the system computationally 'stiff' for control design purposes and also for real-time/online control implementations. The inherent time scale nature of transmission lines are not well addressed in the IEEE 738 Standard, and require a better understanding to efficiently calculate ampacity levels based on line temperature. In this paper, a time domain modeling approach is proposed for a short-length transmission line, which captures the time scale nature of transmission lines. A software control design, utilizing the line's time scale behavior, is proposed that mitigates perturbations in a transmission line.