  We compare cosmological hydrodynamical simulations combined with the
homogeneous metagalactic UV background (UVB) of Haardt & Madau (2012) (HM2012)
to observations of the Lyman-alpha forest that are sensitive to the thermal and
ionization state of the intergalactic medium (IGM). The transition from
optically thick to thin photoheating predicted by the simple one-zone,
radiative transfer model implemented by HM2012 predicts a thermal history that
is in remarkably good agreement with the observed rise of the IGM temperature
at z~3 if we account for the expected evolution of the volume filling factor of
HeIII. Our simulations indicate that there may be, however, some tension
between the observed peak in the temperature evolution and the rather slow
evolution of the HeII opacities suggested by recent Hubble Space Telescope/COS
measurements. The HM2012 UVB also underpredicts the metagalactic hydrogen
photoionization rate required by our simulations to match the observed opacity
of the forest at z>4 and z<2.
