Thermoelastic expansion due to frictional heating causes significant changes in contact pressure and temperature in energy dissipation systems such as brakes and clutches. Finite element analysis of such systems tends to be extremely computer-intensive. We here present an alternative implementation of the transient problem, based on the expression of the temperature and stress fields as modal expansions. For its implementation, the method depends upon the availability of solutions of the eigenvalue problem related to thermoelastic instability (TEI). It is demonstrated that computational efficiencies can be achieved by performing the eigenvalue analysis at a limited number of speeds and then using a suitable interpolation procedure. However, care must be taken in the interpolation process, because eigenvalues of the problem tend to be clustered, which complicates the process of identifying corresponding eigenfunction pairs. The method is validated by convergence tests and illustrated by an example of a multidisc clutch.