This paper presents an initial study of rub-induced thermal bow vibration during acceleration or deceleration of a steam turbine rotor. Previous studies of the subject have been limited to constant speed operation, although the problem is often encountered during attempts to bring a rotor up to speed; observations show that acceleration rate is a factor which controls the magnitude of vibrations. Using a relatively simple numerical analysis, the influence of speed transients on rub-induced synchronous vibration is explored. The analysis reveals some significant trends and can help quantify dynamic response to speed changes under the various conditions which cause stator to rotor rubs. The analysis accounts for transient heat conduction within the rotor in the radial and circumferential directions. The result is an instantaneous temperature distribution from which bow of the rotor between the bearings is predicted. The vibration response to mass eccentricity is determined from the amplification factor and proximity of rotor speed to the critical speed. It is assumed that the bow shape and mode shape of the critical speed are similar. The results demonstrate the influence of rub severity, proximity to critical speed, unbalance level, acceleration rate and acceleration direction. In general, the results show that the effects of rubs are aggravated by slow acceleration up or down through a critical or by extended operation just below a critical.