A Vapor Envelope is an ultra-thin-walled vapor chamber that enables a unique combination of lighter weight, lower profile, and lower cost for heat spreading or heat removal applications. It evolved from work done as part of a DARPA program on Thermal Ground Planes. This paper examines a published testing protocol for the measurement of the thermal resistance of thin flexible thermal ground planes. It then applies an adapted version of the published technique to measure the thermal resistance of a vapor envelope and a dimensionally equivalent solid copper heat spreader. Finally, it looks at the implications of a significantly lower thermal resistance for a specific configuration. The analysis of whether this adapted technique would provide a sufficient metric for industrial application identified the control and understanding of the thermal interface materials as a key determinate. A comparison of the measured thermal resistances of the vapor envelope and copper, for this configuration, demonstrated significantly lower heat source temperatures resulting from significantly lower thermal resistances in the vapor envelope at higher power input levels. It also demonstrated the complex behavior of the vapor envelope with its thermal resistance varying with power input levels.