The formation of local regions of the high-temperature, high-pressure plasma, 'hot-spots', in a vacuum spark is studied using X-ray spectroscopy and holography. Measurements of the dimensions of the hot-spots, of the absolute flux of radiation and of the spectral composition of the X-ray emission, have been analysed to give order-of-magnitude values for the local electron density, temperature and plasma lifetime. It appears that the plasma pressure is >or approximately=10⁷ atm and that the formation of the hot spots requires intense heating rates more commonly associated with focused laser beams, i.e. >or approximately=10¹⁵ W cm^-3. It is probable that in the vacuum spark electron beams are responsible for plasma heating. Possible mechanisms for concentrating energy deposition in localised regions are discussed.