We search for hidden-photon cold dark matter (HP-CDM) using a spectroscopic system in a K-band frequency range. Our system comprises a planar metal plate and cryogenic receiver. This is the first time a cryogenic receiver has been used in the search for HP-CDM. Such use helps reduce thermal noise. We recorded data for 9.3 hours using an effective aperture area of 14.8 cm$^2$. No signal was found in the data. We set upper limits for the parameter of mixing between the photon and HP-CDM in the mass range from 115.79 to 115.85 $mu$eV, $chi < 1.8$-$4.3 times 10^{-10}$, at a 95% confidence level. This is the most stringent upper limit obtained to date in the considered mass range.
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