We report results from a new HST campaign that targets the O vi \lambda \lambda 1032 , 1038 Å doublet in emission around intensely star-forming galaxies . The programme aims to characterize the energy balance in starburst galaxies and gas cooling in the difficult-to-map coronal temperature regime of 2 - 5 \times 10 ^ { 5 } Kelvin . We present the first resolved image of gas emission in the O vi line . Our target , SDSS J115630.63+500822.1 , is very compact in the continuum but displays O vi emission to radii of 23 kpc . The surface brightness profile is well fit by an exponential with a scale length of 7.5 kpc . This is ten times the size of the photoionized gas , and we estimate that about 1/6 the total O vi luminosity comes from resonantly scattered continuum radiation . Spectroscopy – which closely resembles a stacked sample of archival spectra – confirms the O vi emission , and determines the column density and outflow velocity from blueshifted absorption . The combination of measurements enables a large number of calculations with few assumptions . The O vi regions fill only \sim 10 ^ { -3 } of the volume . By comparing the cooling time with the cloud sound-crossing time , the cooling distance with the size , and the pressure in the O vi and nebular gas , we conclude that the O vi -bearing gas can not have been lifted to the scale height at this temperature , and must be cooling in situ through this coronal temperature regime . The coronal phase contains \sim 1 % of the ionized mass , and its kinetic energy at a given instant is \sim 1 % of the budget set by supernova feedback . However a much larger amount of the gas must have cooled through this phase during the star formation episode . The outflow exceeds the escape velocity and the gas may become unbound , but it will recombine before it escapes and become visible to Lyman ( and O i ) spectroscopy . The mapping of this gas represents a crucial step in further constraining galaxy formation scenarios and guiding the development of future astronomical satellites .