  In this paper we formulate a geometric theory of thermal stresses. Given a
temperature distribution, we associate a Riemannian material manifold to the
body, with a metric that explicitly depends on the temperature distribution. A
change of temperature corresponds to a change of the material metric. In this
sense, a temperature change is a concrete example of the so-called referential
evolutions. We also make a concrete connection between our geometric point of
view and the multiplicative decomposition of deformation gradient into thermal
and elastic parts. We study the stress-free temperature distributions of the
finite-deformation theory using curvature tensor of the material manifold. We
find the zero-stress temperature distributions in nonlinear elasticity. Given
an equilibrium configuration, we show that a change of the material manifold,
i.e. a change of the material metric will change the equilibrium configuration.
In the case of a temperature change, this means that given an equilibrium
configuration for a given temperature distribution, a change of temperature
will change the equilibrium configuration. We obtain the explicit form of the
governing partial differential equations for this equilibrium change. We also
show that geometric linearization of the present nonlinear theory leads to
governing equations that are identical to those of the classical linear theory
of thermal stresses.
