We present a new set of direct numerical simulation data of a passive thermal flow in a turbulent plane Poiseuille flow with constant Prandtl number Pr = 0.71, and mixed boundary conditions. Simulations were performed at Re-tau = 500, 1000, and 2000 for several computational domains in the range of l(x) = 2 pi h to 8 pi h and l(z)= pi h to 3 pi h. As a first key result we found that a length of l(x) = 2 pi h and a width of l(z) = pi is enough to accurately obtain the one-point statistics and the budgets of the thermal kinetic energy, its dissipation and the thermal fluxes. None of them collapse exactly in wall units. On the other hand, the value of the thermal Karman constant grows very slightly with the Reynolds number with a value of K-th = 0.44 for Re-tau = 2000. (C) 2018 Elsevier Ltd. All rights reserved.