My research involves the study of heat diffusion in an optical cable that will be used as a heat source in a low-temperature experiment. The system of study consists of a fiber optical cable coated by a film of liquid helium. This system is cooled to near absolute zero, where quantum mechanical properties of the system are studied by using a laser to send short pulses of light through the cable to evaporate pulses of helium vapor. Doing so requires an optical source. To characterize the vapor pulses, it may be important to consider the flow of thermal energy back into the fiber as well as into the liquid helium film. The system can be modeled by a partial differential equation known as the heat equation. Solving the heat equation with respect to the optical source affects the overall experiment. To solve the equation, I use the FORTRAN programming language along with analytical methods whenever feasible.