The Morton effect (ME) is a thermally induced vibration problem observed in a rotor supported by hydrodynamic bearings. The journal’s synchronous orbiting induces nonuniform viscous heating on its circumference, and the ensuing thermal bow often causes unacceptable vibration levels in the rotor. This paper investigates the influence of the tilting pad journal bearing (TPJB)’s pivot design on the severity and instability speed range of ME vibration. Simulations are conducted with two different types of pivots: cylindrical (CYL) and spherical (SPH), which produce different pad degrees-of-freedom and nonlinear pivot stiffness due to their geometries. The friction between pad and pivot, which only exists with the spherical pivot, is modeled, and its impact on the ME is evaluated. The example rotor model, as obtained from the literature, is single overhung, with experimentally measured excessive vibration and large journal temperature differentials, near 8000 rpm. The bearing and journal are modeled with three-dimensional (3D) finite elements, and the shaft with flexible beam elements for ME simulation. Nonlinear transient simulations are carried out for a wide operating speed range with varying pivot design parameters. Simulation results indicate that the predicted ME instability is sensitive to the pivot shape, pivot flexibility, and pad-pivot friction.