  We report results from a new HST study of the OVI 1032,1038\AA\ 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 x $10^5$K. We present the
first resolved image of gas emission in the OVI line. Our target, SDSS
J1156+5008, is very compact in the continuum but displays OVI emission to radii
of 23 kpc. The surface brightness profile is well fit by an exponential with a
scale of 7.5kpc. This is ten times the size of the photoionized gas, and we
estimate that 1/6 the total OVI luminosity comes from resonantly scattered
continuum radiation. Spectroscopy - which closely resembles a stacked sample of
archival spectra - confirms the OVI emission, and determines the column density
and outflow velocity from blueshifted absorption. The combination of
measurements enables several new calculations with few assumptions. The OVI
regions fill only ~$10^{-3}$ 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 OVI and nebular gas, we conclude that the OVI-bearing gas
cannot 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 ~1% of the ionized mass, and its kinetic energy is currently ~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 OI) spectroscopy.
The mapping of this gas represents a crucial step in further constraining
galaxy formation scenarios and guiding the development of future satellites.
