Heat pipes are devices that transfer heat via phase changes in electronic devices. They can be found in laptops, workstations, and satellites. The device is made of an outer metal shell lined with a porous wick and filled with a working fluid. Heat pipe behavior is predictable and reliable at normal temperatures. However, if the heat pipe is exposed to very low temperatures, the working fluid may freeze and change the behavior of the start-up. In particular, if the ingoing heat flux is too large, the heat pipe may overheat, which can result in permanent damage to the pipe and the device in which it is used. In this project, we attempted to numerically simulate the start-up behavior of a conventional heat pipe from a frozen state using transient finite element method within the MOOSE framework. Specifically, we successfully modeled liquid-phase fluid ow and solid-liquid phase change of the working fluid. Additionally, we explored potential methods for liquid-vapor phase change and created a heat pipe mesh that consists of all the parts common for a conventional heat pipe.