This paper investigates the journal asymmetric temperature-induced thermal bow vibration of a rotor, as supported by a flexure pivot journal bearing (FPJB). Thermal bow-induced vibration, known as the Morton effect (ME), is caused by non-uniform viscous heating of the journal, and the resulting thermal bow often causes increasing vibration amplitudes with the time-varying phase. Full FPJB’s structural and thermal finite element models are developed and integrated into the flexible rotor model. The model is validated by comparing its predicted ME response with experimental results. An FPJB model, which uses predicted “equivalent” radial and tilting stiffness of the bearing, is compared with the full finite element method (FEM)-based model. The impact of FPJB’s design parameters such as web thickness, bearing material, and housing thicknesses are investigated with parametric studies. The results show that FPJB parameter values may have a major effect on the speed range of ME vibration, and its severity.