The two-phase closed thermosyphon (TPCT) or wickless heat pipe has been widely considered as an extremely effective and low-cost heat removal device for various applications. A computational fluid dynamics (CFD) investigation of the TPCT can provide detailed information regarding its design and development. In this study, the effect of non-uniform heat-input profiles on a vertical TPCT has been investigated. A CFD model has been built to simulate the evaporation and condensation processes within the TPCT investigated, using a solver based on OpenFOAM which has been modified and validated against experimental data reported in the open literature. Four non-uniform heating profiles of the TPCT have been investigated, and the effects these have on the internal flow field within the pipe are discussed. Simulation results show that the non-uniform heat flux profiles can impact thermal performance depending on the overall heat loading and the heat flux profile.