  The standard cooling scenario in the presence of nucleon superfluidity fits
rather well to the observation of the neutron stars. It implies that the
stellar cooling arguments could place a stringent constraint on the properties
of novel particles. We study in particular the cooling rate induced by dark
gauge bosons for very young neutron stars: remnants of Cassiopeia A and
SN1987A. The cooling is dominantly contributed either by the nucleon pair
breaking and formation in the core or by the electron bremsstrahlung in the
crust, depending on the age of the stars and the form of the couplings. We
compute how much the cooling curve of the young neutron stars could be modified
by the extra dark gauge boson emission and obtain the bound for the dark gauge
boson when its mass is lower than $\mathcal{O}(0.1)\,{\rm MeV}$; for the dark
photon we find the mixing parameter times its mass $\varepsilon
m_{\gamma^\prime} < 1.5 \times 10^{-8}\,{\rm MeV}$ and for the ${\rm
U}(1)_{B-L}$ gauge boson its coupling to nucleons and electrons $e^\prime <
10^{-13}$. We also discuss the possibility that the rapid cooling of Cas A
might provide a hint for the existence of the ${\rm U}(1)_{B-L}$ gauge boson.
