Using hydrodynamical simulations coupled to a radiative transfer code, we study the additional heating effects in the intergalactic medium (IGM) produced by $z\sim 6$ quasars in their near-zones. If helium is predominantly in HeII to begin with, both normalization ($T_0$) and slope ($\gamma$) of the IGM effective equation-of-state get modified by the excess ionization from the quasars. Using the available constraints on $T_0$ at $z\sim6$, we discuss implications for the nature and epoch of HI and HeII reionization. We study the extent of the HeIII region as a function of quasar age and show, for a typical inferred age of $z \sim 6$ quasars (i.e. $\sim 10^8$ yrs), it extends up to 80% of the HI proximity region. For these long lifetimes, the heating effects can be detected even when all the HI lines from the proximity region are used. Using the flux and curvature probability distribution functions (PDFs), we study the statistical detectability of heating effects as a function of initial physical conditions in the IGM. For the present sample size, cosmic variance dominates the flux PDF. The curvature statistics is more suited to capturing the heating effects beyond the cosmic variance, even if the sample size is half of what is presently available.