  We have run a new suite of simulations that solve hydrodynamics and radiative
transfer simultaneously to study helium II reionization. Our suite of
simulations employs various models for populating quasars inside of dark matter
halos, which affect the He II reionization history. In particular, we are able
to explore the impact that differences in the timing and duration of
reionization have on observables. We examine the thermal signature that
reionization leaves on the IGM, and measure the temperature-density relation.
As previous studies have shown, we confirm that the photoheating feedback from
helium II reionization raises the temperature of the IGM by several thousand
kelvin. To compare against observations, we generate synthetic Ly$\alpha$
forest sightlines on-the-fly and match the observed effective optical depth
$\tau_{\mathrm{eff}}(z)$ of hydrogen to recent observations. We show that when
the simulations have been normalized to have the same values of
$\tau_\mathrm{eff}$, the effect that helium II reionization has on observations
of the hydrogen Ly$\alpha$ forest is minimal. Specifically, the flux PDF and
the one-dimensional power spectrum are sensitive to the thermal state of the
IGM, but do not show direct evidence for the ionization state of helium. We
show that the peak temperature of the IGM typically corresponds to the time of
90%-95% helium ionization by volume, and is a relatively robust indicator of
the timing of reionization. Future observations of helium reionization from the
hydrogen Ly$\alpha$ forest should thus focus on measuring the temperature of
the IGM, especially at mean density. Detecting the peak in the IGM temperature
would provide valuable information about the timing of the end of helium II
reionization.
