Cross-linked elastomers have numerous applications including automobiles, sporting goods, and biomedical devices. During both their processing and application, these materials experience large mechanical stresses and thermal gradients. In this study, we investigate the mechanical, optical and thermal transport behavior of a well-defined, cross-linked polybutadiene. This material has been prepared by cross linking a well-entangled and nearly mono-disperse polybutadiene using an organic peroxide cross-linking agent at low concentration. We report linear viscoelastic measurements of this system at various stages of cross-linking. Samples obtained after nearly complete conversion of the cross-linking agent, which can be characterized as lightly cross-linked (i.e., more than 10 entanglements per cross-link), were subjected to a series of large strain, uniaxial deformations. Measurements of the tensile stress and two components of the thermal conductivity tensor will be reported as a function of elongation. These data are also used to examine the stress-thermal rule in which the stress and thermal conductivity tensors are linearly related.