The problem of heat conductivity of laminated shells through the heat-conducting layer in the case of debonding between laminas is formulated. The approach consists in considering a change of layer thickness in the process of debonding and shells deformation. Three dimensional equations of thermoelasticity and heat conduction are expanded into a polynomial Legendre series in terms of the thickness. The firstapproximations equations have been studied in more details. Numerical example of the heat conductivity of the laminated shells through the heat-conducting layer is considered.