[en] Many different turbulent heat transfer calculations based on a very accurate pseudo-spectral code have been performed in the last 5 years. The main effort was to investigate temperature fields at different Prandtl numbers, ranging from Pr=0.7 to Pr=200. For the treatment of the turbulent heat transfer at low Reynolds and high Prandtl numbers, a Direct Numerical Simulation (DNS) was used for structures of the turbulent motions. DNS describes all the length and time scales for velocity and temperature fields. When Prandtl number is higher than 1, the smallest temperature scales are approximately inversely proportional to the square root of Prandtl number. For the smallest temperature scales, not resolved in the high Prandtl number simulation, a spectral turbulent diffusivity model was used in the pseudo-spectral computer code for DNS. A comparison of our temperature profiles obtained at friction Reynolds number Reτ=150 and Pr=100 and Pr=200 to the mean profiles of Calmet and Magnaudet, Wang and Lu and Kader's correlation that was built as a best fit of various experimental data at higher Reynolds numbers, revealed the discrepancies up to 10%. The most important reason for the differences was in different Reynolds numbers, which were much lower in our simulations than in the above mentioned LES simulations and experiments. The similar phenomenon as in our case can be found when DNS of Kawamura and Kader's results at Reτ=180 and Pr=0.71 were compared. On the other hand, the comparisons to the Kader's correlation at higher Reynolds numbers (i.e. DNS of Kawamura at Reτ=640 and DNS of Tiselj at Reτ=424) show that the differences are within statistical uncertainties. It follows that the heat transfer depends much more on Reynolds number in the range of low Reynolds numbers than in the range of high Reynolds numbers. (author)