  We investigate the spectroscopic properties of the strange particle kaon in
the framework of hot and dense QCD. To this end, first, we find the
perturbative spectral density, which is connected with both the temperature $T$
and the baryon chemical potential $\mu_{B}$. We include the non-perturbative
operators as functions of temperature and baryon chemical potential up to mass
dimension five. We perform the calculations in momentum space and use the quark
propagator in the hot and dense medium. The numerical results at non-zero
temperature and baryon chemical potential demonstrate that the mass of the
particle rises considerably by increasing the baryon chemical potential at a
fixed temperature (for both the zero and non-zero temperatures) up to
approximately $\mu_{B}=0.4$ GeV. After this point, it starts to fall by
increasing the baryon chemical potential and it apparently vanishes at
$\mu_{B}=(1.03-1.15)$ GeV for finite temperatures: The point of apparent
vanishing moves to lower baryon chemical potentials by increasing the
temperature. At zero temperature, the mass reaches to roughly a fixed value at
higher baryon chemical potentials. On the other hand, the decay constant
decreases considerably with respect to baryon chemical potential up to roughly
$\mu_{B}=0.4$ GeV, but after this point, it starts to increase in terms of the
baryon chemical potential at finite temperatures. At $T=0$, the decay constant
reaches to a fixed value at higher chemical potentials, as well. Regarding the
dependence on the temperature we observe that, at fixed values of baryon
chemical potentials, the mass and decay constant remain roughly unchanged up to
$T=50$ MeV and $T=70$ MeV respectively, but after these points, the mass starts
to fall and the decay constant starts to rise up to a critical temperature
$T=155$ MeV, considerably.
