  The thermal dynamics in thermo-mechanical systems exhibits a much slower time
scale compared to the structural dynamics. In this work, we use the method of
multiple scales to reduce the thermo-mechanical structural models with a
slowly-varying temperature distribution in a systematic manner. In the process,
we construct a reduction basis that adapts according to the instantaneous
temperature distribution of the structure, facilitating an efficient reduction
in the number of unknown. As a proof of concept, we demonstrate the method on a
range of linear and nonlinear beam examples and obtain a consistently better
accuracy and reduction in the number of unknowns than standard the Galerkin
projection using a constant basis.
