We present the development, coupling, and application of a quasi-3D multiphysics model of a notional all electric ship electromagnetic launcher (EML) and a dynamic parallel-flow heat exchanger (PFHX) model to devise effective thermal management strategies for naval EMLs. The EML model combines a 2D electromagnetic thermal model and a 3D thermal-fluid model developed based on the fundamental laws of electromagnetism, heat transfer, and fluid dynamics. Similarly, we applied the conservation laws to formulate a PFHX model and nondimensionalized it by identifying dimensionless parameters that pertained to the effectiveness-NTH method. We solved the coupled EML-PFHX model using finite element method and employed it to investigate the following aspects of naval EML thermal management: the effects of (1) thermal diffusion in the rail, (2) PFHX design and operation, and (3) cooling channel location on cooling performance and heat reversal. Subsequently, we deduced the following from our study: (1) thermal diffusion effectively assists the cooling channel with peak temperature reduction, and its contribution to the determination of optimal channel allocation is non-trivial; (2) improvement in cooling performance is not always directly proportional to larger heat exchanger size and higher flow rate increased flow rate and NTU only result in higher pumping power as well as heat exchanger cost and volume without significant improvement in cooling performance beyond the optimal design and operating point; (3) placing the cooling channel close to the initial hot spot in the rail yields inferior cooling performance at high mass flow rate with 10 s of cooling and exacerbates the heat-reversal effect; and (4) optimal cooling channel allocation must therefore base on the given mass flow rate and cooling period placing the channel near the initial hot spot is favorable for lower mass flow rates and shorter cooling periods, whereas channels should be placed at the rail center for equidistant heat flow from all four corners in the opposite case.