The Magellanic Stream ( MS ) is a nearby laboratory for studying the fate of cool gas streams injected into a gaseous galactic halo . We investigate properties of the boundary layer between the cool MS gas and the hot Milky Way halo with 21 cm H i observations of a relatively isolated cloud having circular projection in the northern MS . Through averaging and modeling techniques , our observations obtained with the Robert C. Byrd Green Bank Telescope ( GBT ) , reach unprecedented 3 \sigma sensitivity of \sim 1 \times 10 ^ { 17 } cm ^ { -2 } , while retaining the telescope ’ s 9.1 ^ { \prime } resolution in the essential radial dimension . We find an envelope of diffuse neutral gas with \text { FWHM } \text { of } 60 \text { km } \text { s } ^ { -1 } , associated in velocity with the cloud core having \text { FWHM } \text { of } 20 \text { km } \text { s } ^ { -1 } , extending to 3.5 times the core radius with a neutral mass seven times that of the core . We show that the envelope is too extended to represent a conduction-dominated layer between the core and the halo . Its observed properties are better explained by a turbulent mixing layer driven by hydrodynamic instabilities . The fortuitous alignment of the ( catalog NGC 7469 ) background source near the cloud center allows us to combine UV absorption and H i emission data to determine a core temperature of 8350 \pm 350 \text { K } . We show that the H i column density and size of the core can be reproduced when a slightly larger cloud is exposed to Galactic and extragalactic background ionizing radiation . Cooling in the large diffuse turbulent mixing layer envelope extends the cloud lifetime by at least a factor of two relative to a simple hydrodynamic ablation case , suggesting that the cloud is likely to reach the Milky Way disk .