The coupling efficiency of short-pulse ignition laser energy to hot-spot internal energy directly affects the feasibility of fast ignition. Experimental characterization of the hot spot has attracted much attention. Among temperature, density and neutron yield of fast ignition experiments, the temperature of the hot spot has few available diagnostic methods. Multispectral X-ray imaging of hot-spot continuum emission is expected to give the time evolution of the electron temperature distribution. This article describes electron temperature determination from multispectral imaging, a dual-channel X-ray Kirkpatrick-Baez (KB) microscope designed for two-spectral imaging, and the experimental results of hot-core multispectral imaging of an imploded cone-shell target at the SG-II laser facility.