The thermal conductivity λ of amorphous, crystalline, and liquid selenium (purity 99,99999 %) is measured in the temperature range 80 to 525°K which includes the softening (T ≈ 31°C) and melting points. The thermal conductivity of amorphous selenium increases linearly with temperature up to 304°K at which temperature there is a discontinuity involving a sharp increase of about 40%. Admixtures of Cd and Tl change the values of the discontinuity Δλg and temperature Tg. An admixture of Cd shifts the value of Δλg from 0.44 × 10−3 to 0.11 × 10−3 cal/(cm s degree) and increases Tg from 30.7 to 33.5°C. Heat treatment increases λ and changes its temperature profile. Admixtures of Tl remove the discontinuity. The thermal conductivity of selenium during melting undergoes a discontinuity of about 40% which is explained by the increase in the intermolecular distance from 3.46 to 3.74 Å. A photon thermal conductivity, which accounts for up to 30% of the overall thermal conductivity, is found in crystalline selenium at temperatures above about 350°K. The experimentally determined value of λ, its temperature dependence, the values of the softening and melting discontinuities and the photon parts agree well with theory.