Compliant conduction rail assembly and method are provided for facilitating cooling of an electronics structure. The rail assembly includes a first thermally conductive rail mounted to a surface of the electronics structure, a second thermally conductive rail thermally conductively interfaced to the first rail, and a biasing mechanism biasing the second rail away from the first rail. The first and second rails and the biasing mechanism are configured for slidable insertion into a housing with the electronics structure, the housing containing a liquid-cooled cold plate(s). With insertion of the electronics structure into the housing, the second rail engages the liquid-cooled cold plate and is forced by the biasing mechanism into thermal contact with the cold plate, and is forced by the cold plate towards the first rail, which results in a compliant thermal interface between the electronics structure and the liquid-cooled cold plate of the housing.