The present study discusses the deviation from the pure dead-time model of passive scalars such as temperature and concentration in the Poiseulle flow Even in the case of no thermal diffusion, there exists a substantial amount of damping and large deviation of phase lag from that computed by the traditional dead-time model after only 10 diameter downstream. These are caused by the phase difference of temperature in the radial direction due to the nonuniform velocity distribution. In the presence of thermal diffusion, damping is more pronounced.