Molecules of a substance (or thermal markers) in a turbulent flow escape from the fluid particles in which they are released because of their molecular diffusivity. The consequences of this phenomenon on the effectiveness of turbulence to disperse a foreign substance are explored by using a Direct Numerical Simulation (DNS) of flow in a channel. Trajectories of molecules of different Schmidt (or Prandtl) numbers originating in the center of the channel are computed and property autocorrelations and other single-particle Lagrangian statistics are reported and discussed.