With the development of high temperature gas-cooled reactors, gases are strongly heated near the wall region in the reactor core or steam generator tubes. Large temperature difference between the wall and the gas will result in dramatic property variations in the cross section, which will influence both friction factors and heat transfer coefficients. As thermal conductivity, specific heat capacity, density, and viscosity of gas are all sensitive to temperature, analysis of property variation effects on turbulent convection is really complex. Most existing correlations use wall to bulk fluid temperature ratio (T_w/T_b) to take account of property variation effects on friction factors and Nusselt numbers. An exponential function of T_w/T_b is used to modify the constant property correlation. The exponent is obtained by regression analysis of experimental data, which depends on heating or cooling conditions and on the kinds of gases. In the current investigation, the influence of property variation on velocity and temperature fields are simplified as the influence on the critical point between the linear and the logarithmic distribution regions. New correlations for velocity and temperature distributions are obtained, which show good prediction of measured velocity and temperature magnitude in the literature. Based on the correlations for velocity and temperature distributions, new friction factors and Nusselt number correlations are obtained. The derived friction factor correlation agrees well with the conventional correlation in the literature. The derived Nusselt number correlation agrees well with the experimental data, which can be used both for nitrogen and helium-xenon mixture.