Direct numerical simulations of the velocity and temperature fields for turbulent flow in a channel are used to examine the influence of Prandtl number Pr on turbulent transport. The Reynolds number, based on the half-height of the channel and the friction velocity, is Re_τ = 150. Prandtl numbers of 1.0, 0.3, 0.1, 0.05, 0.025 were studied. The bottom and the top walls were kept at constant temperatures of +T_w and −T_w. The influence of Pr on Reynolds transport, on the turbulent diffusivity, α_τ, and on the spectral density function of the temperature fluctuations was studied. The observation that spatial variations of the ratio of the turbulent diffusivity to the value observed at Pr = 1.0 are not large is used to propose a method for calculating average temperature fields. The decrease in α_τ with decreasing Pr is related to observations of the increased damping of high-wavenumber temperature fluctuations. Molecular conductivity, at smaller Pr, is pictured to act as a filter that renders high-frequency velocity fluctuations ineffective in transporting heat.