We analyze and compute the semiclassical stress-energy flux components, the outflux $langle T_{uu}rangle$ and the influx $langle T_{vv}rangle$ ($u$ and $v$ being the standard null Eddington coordinates), at the inner horizon (IH) of a Reissner-Nordstrom black hole (BH) of mass $M$ and charge $Q$, in the near-extremal domain in which $Q/M$ approaches $1$. We consider a minimally-coupled massless quantum scalar field, in both Hartle-Hawking ($H$) and Unruh ($U$) states, the latter corresponding to an evaporating BH. The near-extremal domain lends itself to an analytical treatment which sheds light on the behavior of various quantities on approaching extremality. We explore the behavior of the three near-IH flux quantities $langle T_{uu}^-rangle^U$, $langle T_{vv}^-rangle^U$, and $langle T_{uu}^-rangle^H=langle T_{vv}^-rangle^H$, as a function of the small parameter $Deltaequivsqrt{1-(Q/M)^2}$ (where the superscript $-$ refers to the IH value). We find that in the near-extremal domain $langle T_{uu}^-rangle^Uconglangle T_{uu}^-rangle^H=langle T_{vv}^-rangle^H$ behaves as $proptoDelta^5$. In contrast, $langle T_{vv}^-rangle^U$ behaves as $proptoDelta^4$, and we calculate the prefactor analytically. It therefore follows that the semiclassical fluxes at the IH neighborhood of an evaporating near-extremal spherical charged BH are dominated by the influx $langle T_{vv}rangle^U$. In passing, we also find an analytical expression for the transmission coefficient outside a Reissner-Nordstrom BH to leading order in small frequencies (which turns out to be a crucial ingredient of our near-extremal analysis). Furthermore, we explicitly obtain the near-extremal Hawking-evaporation rate ($proptoDelta^4$), with an analytical expression for the prefactor (obtained here for the first time to the best of our knowledge). [Abridged]
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