The influence upon the temperature distribution within a hydrodynamically lubricated journal bearing of a time varying journal orbit is considered and the oscillatory source distribution arising as a result of unsteady shearing of the lubricant is examined with respect to axes which rotate with the journal. The time dependent thermal bend induced in a rotor by such a process has been evaluated and incorporated into a rotor dynamic model for the assessment of system stability. Techniques have been developed enabling calculations to be carried out on an idealized rotor-bearing configuration and the speed range over which instability occurred was established. The rate of growth of the unstable vibrations together with the rate and direction of `spiralling' of the thermal bend vector were also determined. Features of rotor and bearing design having an influence on such thermally induced instability are assessed.