Integrating the cooling systems of power electronics and electric machines (PEEMs) with other existing vehicle thermal management systems is an innovative technology for the next-generation hybrid electric vehicles (HEVs). As such, the reliability of PEEM must be assured under different dynamic duty cycles. Accumulation of excessive heat within the multilayered packages of PEEMs, due to the thermal contact resistance between the layers and variable temperature of the coolant, is the main challenge that needs to be addressed over a transient thermal duty cycle. Accordingly, a new analytical model is developed to predict transient heat diffusion inside multilayered composite packages. It is assumed that the composite exchanges heat via convection and radiation mechanisms with the surrounding fluid whose temperature varies arbitrarily over time (thermal duty cycle). As such, a time-dependent conjugate convection and radiation heat transfer is considered for the outer-surface. Moreover, arbitrary heat generation inside the layers and thermal contact resistances between the layers are taken into account. New closed-form relationships are developed to calculate the temperature distribution inside multilayered media. The present model is used to find an optimum value for the angular frequency of the surrounding fluid temperature to maximize the interfacial heat flux of composite media; up to 10% higher interfacial heat dissipation rate compared to constant fluid-temperature case. An independent numerical simulation is also performed using Comsol Multiphysics; the maximum relative difference between the obtained numerical data and the analytical model is less than 6%.