Under normal operation, a rotor levitated by magnetic bearings will rotate without making contact with any stator component. However, there are a number of circumstances that may lead to temporary or permanent loss of levitation. These include full rotor drop events arising from power loss, momentary fault conditions, sudden changes in unbalance, high levels of base acceleration, and other aerodynamically induced force inputs. The spinning rotor will come into dynamic contact with an auxiliary bearing. Highly localized and transient temperatures will arise from frictional heating over the dynamically varying contact area. Rotor dynamic contact forces are predicted for a range of initial conditions leading to combinations of bounce and rub motion on the auxiliary bearing. The transient heat flux from the contact area is then ascertained. A transient thermal Green’s function is developed in a form that is effective over short or long time scales and local to the source. This enables the transient thermal response of an auxiliary bearing to be assessed for a range of dynamic contact conditions. Auxiliary bearings consisting of fixed bushings and free to rotate inner races are analyzed. The results show that significant localized contact temperatures may arise from each contact event, which would accumulate for multiple contact cases. The methodology will be of relevance for the life prediction of auxiliary bearing designs.