The Morton effect (ME) is a thermally induced instability problem that most commonly appears in rotating shafts with large overhung masses, outboard of the bearing span. The time-varying thermal bow due to the asymmetric journal temperature distribution may cause intolerable synchronous vibrations that exhibit a hysteresis behavior with respect to rotor speed. The fully nonlinear transient method designed for the ME prediction, in general, overhung rotors is proposed with the capability to perform the thermoelastohydrodynamic analysis for all the bearings and model the rotor thermal bow at both overhung ends with equivalent distributed unbalances. The more accurate nonlinear, coupled, double overhung approach is shown to provide significantly different response prediction relative to the more approximate linear method based using bearing coefficients and the single-overhung method, which assumes that the ME on both rotor ends can be decoupled. The flexibility of the bearing pad and pivot is investigated to demonstrate that the pivot flexibility can significantly affect the rotordynamics and ME, while the rigid pad model is generally a good approximation.