The intrinsic carrier density of 4H-SiC at temperatures ranging from 294 to 595 K was derived by analyzing a collector current in an npn-type SiC bipolar junction transistor, the structure of which was designed based on a device simulation. The obtained intrinsic carrier density was in good agreement with the value calculated from the bandgap and effective densities of states taking multiple and non-parabolic SiC bands into account. The coincidence of the intrinsic carrier density obtained by these two different approaches indicates the usefulness of the proposed method and the validity of the evaluated value of intrinsic carrier density. The temperature dependence of the bandgap was also estimated from the deduced intrinsic carrier density and compared with an empirical formula. The derived bandgap agreed well with the empirical formula showing bandgap shrinkage at high temperatures. The errors in evaluating the intrinsic carrier density and the bandgap caused by the estimation of the hole density and electron mobility in the base layer are also discussed for the proposed method.