Direct numerical simulations (DNSs) in a turbulent channel flow are used to examine the behavior of the turbulent Prandtl number Pr-t for air (Pr = 0.71) and mercury (Pr = 0.025), with a view to calculating the mean temperature. Constant time-averaged (surface) heat flux (CHF) is used as a thermal boundary condition. For each Pr, four values of the Karman number (h(+) = 180, 395, 640, 1020) are used. Datasets for the constant heating source (CHS) are also examined. For Pr = 0.71, Prt is approximately 1.1 at the wall, varies between 0.9 and 1.1 in the region y(+) <100, and is approximated by 0.9-0.3(y/h)(2) for y/h > 0.2. The latter relation, with a low Re correction term (i.e. 25/h(+)), yields an excellent prediction for the mean temperature up to h(+) = 2000, whereas a calculation based on Pr-t = 0.85 underestimates the mean temperature. The calculated maximum wall-normal turbulent heat flux and Nusselt number also agree well with the empirical relations over a wide range of h(+). For Pr = 0.025, Prt departs significantly from unity inside the inner region (y/h < 0.2) owing to the strong conductive effect, whilst the magnitude in the outer region (y/h > 0.2) tends to approach that corresponding to Pr = 0.71 as h+ increases due to the increase in the Peclet number. The h(+) dependence of Prt in the logarithmic and outer regions is represented adequately by the turbulent Peclet number, i.e. Per = Pr(v(t)/y). The resulting Pr, relation, which is an extension of the expression established by Kays (1994), leads to a correct calculation of the mean temperature not only for mercury (Pr = 0.025) but also for liquid sodium (Pr = 0.01). The mean temperature defect profile exhibits an outer-layer similarity when Pe( RebPr)> 2000; the Nusselt number is represented by Nu = 4.8 + 0.0147Pe(0.84) reasonably well. (C) 2018 Elsevier Ltd. All rights reserved.