We present a systematic QCD sum-rule analysis of the in-medium properties of the charged kaon doublet $K^{\pm }$ over the full $(T,\rho )$ plane relevant to current and forthcoming heavy-ion experiments. Working within the QCD sum-rule framework and incorporating temperature- and density-dependent quark, gluon, and mixed condensates, we derive Borel-transformed sum rules for the effective masses $m_{K^{\pm }}$, the pseudoscalar decay constants $f_{K^{\pm }}$, and the vector self-energy ${\mathrm{\Sigma }}_v$ of both charged states simultaneously. Our vacuum results, $m_{K^{-}}={494.6}_{-6.9}^{+4.9}\mathrm{MeV}$ and $f_{K^{-}}={157.3}_{-2.9}^{+4.1}\mathrm{MeV}$ (with near-degenerate $K^{+}$ values), are in excellent agreement with Particle Data Group values at the subpercent level. In the medium, $m_{K^{\pm }}$ decreases monotonically with increasing baryon density and temperature, signaling progressive partial restoration of chiral symmetry. A pronounced mass splitting $\mathrm{\Delta }m=m_{K^{-}}-m_{K^{+}}$ develops in baryonic matter, driven by the opposite sign of the Weinberg–Tomozawa vector interaction for the two charge states; it reaches $|\mathrm{\Delta }m|\sim 0.35\mathrm{GeV}$ near $\rho \simeq 3.2{\rho }_{\mathrm{sat}}$ at $T=0$ and is partially quenched by thermal fluctuations. A central outcome of this study is the extraction of the critical onset density ${\rho }_c$, defined as the threshold beyond which the in-medium modifications of $K^{-}$ properties signal the onset of the transition toward the chirally restored phase. We stress that ${\rho }_c(T)$ should not be interpreted as a precise determination of the QCD critical point—a task beyond the reach of any current effective framework—but rather as an indicator of the density regime where hadronic descriptions begin to break down and quark degrees of freedom become increasingly relevant. With this interpretation, our results reveal a pronounced temperature dependence: ${\rho }_c\simeq (1.2–1.4){\rho }_{\mathrm{sat}}$ for $T\lesssim 100\mathrm{MeV}$, reflecting the robustness of the hadronic phase under cold compression, and a sharp reduction to ${\rho }_c\simeq 0.45{\rho }_{\mathrm{sat}}$ near the pseudocritical temperature $T_c\simeq 155\mathrm{MeV}$. This dramatic downward shift reflects the synergistic destabilization of the chiral condensate by combined thermal and density fluctuations, and establishes temperature as a more efficient driver of chiral restoration than baryon density alone in the regime accessible to current experiments. Our findings provide quantitative, QCD-based theoretical input for interpreting kaon observables at HADES/GSI, CBM/FAIR, STAR/RHIC, and NA61/SHINE/CERN-SPS, and carry direct implications for kaon condensation in neutron star matter and the hadronic equation of state at supranuclear densities.

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• Particle interactions
• Strong interaction
• Sum rules
• Kaons
• Finite temperature field theory