Flexible electronic devices generally integrate inorganic materials on a polymer substrate (such as metal films on a deformable polymer). The properties of these inorganic/organic hybrids are of great practical and theoretical. There have been numerous experimental and theoretical study of their mechanical properties, especially the failure strain of polymer-supported metal films. The fracture strain of polymer-supported thin metal films is significantly higher than that of free-standing metal films due to the suppressed necking in the supported metal film. However, there are few studies of the thermal conductivity of extremely strained metal films and inorganic/organic hybrids. Here, we experimentally measure the thermal conductivity of extremely strained polyimide-supported Au nanofilms (100 nm Au on 25.4 µm polyimide). The systematic study of interrelated mechanical, electrical, and thermal properties leads to a better understanding of the performance of flexible electronic devices across a range of realistic operating conditions. In addition, the validity of Wiedemann-Franz law for extremely strained metal is evaluated by comparing the measured thermal and electrical conductivities.