This paper presents theoretical models and simulation results for the synchronous, thermal transient, instability phenomenon known as the Morton effect. A transient analysis of the rotor supported by tilting pad journal bearing is performed to obtain the transient asymmetric temperature distribution of the journal by solving the variable viscosity Reynolds equation, a 2D energy equation, the heat conduction equation, and the equations of motion for the rotor. The asymmetric temperature causes the rotor to bow at the journal, inducing a mass imbalance of overhung components such as impellers, which changes the synchronous vibrations and the journal's asymmetric temperature. Modeling and simulation of the cyclic amplitude, synchronous vibration due to the Morton effect for tilting pad bearing supported machinery is the subject of this paper. The tilting pad bearing model is general and nonlinear, and thermal modes and staggered integration approaches are utilized in order to reduce computation time. The simulation results indicate that the temperature of the journal varies sinusoidally along the circumferential direction and linearly across the diameter. The vibration amplitude is demonstrated to vary slowly with time due to the transient asymmetric heating of the shaft. The approach's novelty is the determination of the large motion, cyclic synchronous amplitude behavior shown by experimental results in the literature, unlike other approaches that treat the phenomenon as a linear instability. The approach is benchmarked against the experiment of de Jongh.