Thermal state of the intergalactic medium near to the optical limit for
  the Ly-$\alpha$ forest
  In this article, the temperature-density relation of the intergalactic medium
was studied in the region $1.6 \leq z < 2.0$ divided into two bins. For this
purpose, the Ly-$\alpha$ forest decomposition into individual absorption
profiles was used for the study of 35 publicly available quasar spectra
obtained by the Ultraviolet and Visual Echelle Spectrograph (UVES) on the Very
Large Telescope (ESO) and by the High Resolution Echelle Spectrometer (HIRES)
on the Keck Telescope. For the determination of the thermal state sensitive
cut-off position in the $b - N_{HI}$ distribution, the iterative fitting
procedure was adopted. The measurements were calibrated using mock Ly-$\alpha$
forest data generated by 23 hydrodynamical simulations with different thermal
histories. The value of the temperature at mean density corresponds to the
decreasing trend predicted by various models at the lower redshifts. In the
case of power law index, determined values are close to 1.6, which is expected
after all reionization events in various models assuming the balance of
photoheating with adiabatic cooling.
