Abstract: The expression of the so called eollisionless electron heat conduction, which was proposed by Hollweg in 1976 based on the qualitative analysis, is deduced from the moment equations of the electron distribution function under the assumption of the existence of the polytrope law between the electron thermal pressure and electron density. Comparison of the expression deduced here with the Hollweg’s expression indicates that the unknown dimensionless factor in the letter is determined by the poly-trope index. The applicability of the "collisionless electron heat conduction" and the mechanism of the electron heat transport in the solar wind are discussed in detail.