**Abstract:** We prove global existence for a simplified
model of one-dimensional thermoelasticity. The governing
equations satisfy the balance of momentum and a modified energy
balance. The application we wish to study by investigating this
model are shape-memory alloys. They are a prominent example of
solids undergoing structural phase transitions. A characteristic
feature of these materials is that several crystalline variants
are stable at low temperature. Consequently, the free energy
considered here is nonconvex as a function of the deformation
gradient for temperatures below a fixed threshold
temperature. As a result of the nonconvexity of the free energy
density, existence of weak solutions is not to be generally
expected. We therefore show existence of a Young measure valued
solution. The proof relies on vanishing capillarity.