The detection of very hot plasma in the quiescent corona is important for diagnosing heating mechanisms. The presence and the amount of such hot plasma is currently debated. The SphinX instrument on-board CORONAS-PHOTON mission is sensitive to X-ray emission well above 1 keV and provides the opportunity to detect the hot plasma component. We analyzed the X-ray spectra of the solar corona collected by the SphinX spectrometer in May 2009 (when two active regions were present). We modelled the spectrum extracted from the whole Sun over a time window of 17 days in the 1.34-7 keV energy band by adopting the latest release of the APED database. The SphinX broadband spectrum cannot be modelled by a single isothermal component of optically thin plasma and two components are necessary. In particular, the high statistics and the accurate calibration of the spectrometer allowed us to detect a very hot component at ~7 million K with an emission measure of ~2.7 x 10^44 cm^-3. The X-ray emission from the hot plasma dominates the solar X-ray spectrum above 4 keV. We checked that this hot component is invariably present both at high and low emission regimes, i.e. even excluding resolvable microflares. We also present and discuss a possible non-thermal origin (compatible with a weak contribution from thick-target bremsstrahlung) for this hard emission component. Our results support the nanoflare scenario and might confirm that a minor flaring activity is ever-present in the quiescent corona, as also inferred for the coronae of other stars.