  We present a Monte-Carlo model of He II reionization by QSOs and its effect
on the thermal state of the clumpy intergalactic medium (IGM). The model
assumes that patchy reionization develops as a result of the discrete
distribution of QSOs. It includes various recipes for the propagation of the
ionizing photons, and treats photo-heating self-consistently. The model
provides the fraction of He III, the mean temperature in the IGM, and the He II
mean optical depth -- all as a function of redshift. It also predicts the
evolution of the local temperature versus density relation during reionization.
Our findings are as follows: The fraction of He III increases gradually until
it becomes close to unity at $z\sim 2.8-3.0$. The He II mean optical depth
decreases from $\tau\sim 10$ at $z\geq 3.5$ to $\tau\leq 0.5$ at $z\leq 2.5$.
The mean temperature rises gradually between $z\sim 4$ and $z\sim 3$ and
declines slowly at lower redshifts. The model predicts a flattening of the
temperature-density relation with significant increase in the scatter during
reionization at $z\sim 3$. Towards the end of reionization the scatter is
reduced and a tight relation is re-established. This scatter should be
incorporated in the analysis of the Ly$\alpha$ forest at $z\leq 3$. Comparison
with observational results of the optical depth and the mean temperature at
moderate redshifts constrains several key physical parameters.
