  The invariance under co-ordinate transformations of a set of partial
differential equations can lead to the possibility of invisibility cloaking,
whereby an anomaly in the interior of a body is shielded from an external
observer. The form invariance of the equations of thermoelasticity under a
class of transformations between reference configurations is demonstrated, with
implications for thermal and thermoelastic invisibility cloaking discussed.
Specifically, the theory of thermoelasticity is found to not allow for
invisibility cloaking, similarly to elastodynamics. Thermal invisibility
cloaking is therefore broken by coupling to mechanics. In the case of weakly
coupled linear thermoelasticity, measurements of temperature by external
observers are shown to be perturbed by the weak thermomechanical coupling, but
only to second order in the degree of coupling. This implies the phenomenon of
approximate invisibility, meaning that a thermal cloaking device with weak
coupling to mechanics could maintain near-perfect cloaking.
