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.