During the EXOSAT observation of 2S1636-536 in July 1983 the quiescent flux was observed to brighten from 1.7×10 -9 ergs/cm. 2 /sec to 2.6×10-9 ergs/cm. 2 /sec, this increase being accompanied by a decrease in effective temperature. Further analysis of the spectrum reveals that the best fit is a power law with an index which increases from -1.75 to-2.1 while the source brightens; there is some evidence for an upper cut off. This spectrum is interpreted as the result of soft photons from the neutron star surface which are Comptonised in a hot plasma cloud surrounding the neutron star (neutron star corona). The increasing spectral index is seen as the result of Compton cooling of the corona as the output of quiescent flux rises in response to an increasing accretion rate.