Spectral emissivity is an essential thermophysical property for optical measurements and radiative transfer analysis. This study develops a measurement system for simultaneously measuring the spectral emissivity and the temperature of samples with low thermal conductivity at high temperatures. A synergistic heating treatment used in the measurement includes a high-power laser and an electric heating radiant cavity. The measurement of spectral radiation intensities is based on a Fourier transform infrared spectrometer, and spectral response functions of the spectrometer is calibrated by a blackbody source with two-temperature method at high temperatures. A method that can simultaneously measure the normal spectral emissivity of continuum spectra and temperature of samples is proposed by the dynamic spectral radiometry. Using reasonable assumptions that the spectral emissivity varies linearly with temperature within a small temperature difference, the dynamic spectral radiation information of the sample is used to construct an overdetermined set of equations each containing the spectral emissivity and the sample temperature as unknowns. Genetic algorithm with large mutations is used to transform the overdetermined equations including temperature and emissivity. Moreover, before performing the experimental measurement of spectral emissivity, the uniformity of temperature distribution on the sample surface and inside the sample is numerically evaluated. The temperature difference of the sample is less than 10.0 K in the studied area. The equipment and method are then validated using measurements on an alumina ceramic fiber sample in the spectral range of 2.5-25.0 µm at temperatures of 673 K, 873 K, 1073 K and 1273 K. The relative uncertainties in the experiment of the alumina ceramic fiber sample at high temperatures are all less than 4.0%. The current study provides a feasible way for simultaneously obtaining the spectral emissivity and temperature of an opaque material with low thermal conductivity, and it is a bold attempt to overcome the difficulty of measuring spectral emissivity at high temperature.