Annular components are used widely in engineering systems and include bearing bushes and races, which may be exposed to extreme operating conditions. A method to establish the localized transient thermoelastic deformation of a homogeneous two-dimensional annular component is developed. The analysis is based on solving the thermoelasticity equations using a state space formulation for the Fourier components of the radial and tangential displacements. Two boundary conditions are considered, namely, rigid and resiliently mounted outer boundaries, both associated with stress free inner boundary conditions. The thermoelastic solution is then demonstrated for a transient temperature distribution induced by inner boundary frictional heating due to rotor contact, which is derived from a dynamic Hertzian pressure distribution. The application is to a relatively short auxiliary bearing for which a state of plane stress is appropriate. However, the thermoelastic analysis is generalized to cover cases of plane strain and plane stress.