A finite element-based technique for coupled thermo-mechanical analysis of woven Ceramic MatrixComposites sheets is presented for the prediction of the degradation of transverse thermal transport behaviour with in-plane extension. The thermal conductivity-strain characteristics have been determined, at the tow level, from the properties of the constituent elements, and then extended to tows and composite. The non-linear thermal conductivity-extension behaviour of the tow has been discretised by multi-linear curves, and implemented in a user-defined subroutine in ABAQUS to model the behaviour of the homogenised orthotropic unidirectional tow and its matrix. By using this approach, an 8-Harness Satin weave HITCO C/C composite unit cell has then been analysed. The variation of through-thickness thermal conductivity degradation with in-plane extension has been predicted and compared with the results of experiments. Very good agreement has been achieved. Two classes of behaviour have been experimentally observed: one that exhibits a brittle response, and another that shows a quasi-ductile behaviour. Both classes of behaviour have been predicted and shown to relate, respectively, to strain localisation and instantaneous pull-out deactivation, without localisation being invoked. These responses are reflected directly in the predicted and experimental rates of decay of transverse thermal conductivity with axial extension. It is advocated that the reduction in transverse thermal conductivity with extension and damage can be used as a Structural Integrity Monitor for CMC operational components.