The SphinX X-ray spectrophotometer on the CORONAS-PHOTON mission observed the 1 - 15 keV X-ray spectrum of the spatially integrated solar corona during the deep minimum of 2009, when solar activity was exceptionally low. Its sensitivity for energies >1.2 keV was higher than that of any other solar X-ray spectrometer in orbit at the time, including the detectors on the Geostationary Operational Environmental Satellites (GOES). Using much improved instrumental data than was used previously, we analysed SphinX spectra in 576 intervals for which there was no discernible activity (NA), 40 intervals when there were X-ray brightenings (B), and 16 intervals when there were micro-flares with peak emission less than GOES A1 (F). An instrumental background spectrum, formed over 34 hours of spacecraft night-time periods and including electronic noise and particle radiation, was subtracted from the solar spectra. Theoretical spectra were used to deduce temperatures on an isothermal assumption for the NA, B, and F intervals (1.69, 1.81, and 1.86 MK, respectively). Differential emission measure (DEM) analysis for the same spectra revealed a "cooler" component (logT =6.2 or T ≈1.6 MK) in each case, but with a second hotter component having a less well-defined peak temperature varying from ≈2.5 to ≈3.5 MK (logT =6.4 and 6.55) and an emission measure between two and three orders smaller than that of the cooler component. These results are similar to those obtained at times just after solar minimum with the EVE instrument. A very hot component that might indicate the signature of nano-flare heating of the corona is not evident in SphinX data.