  Within the framework of the $U(3)$ chiral perturbation theory, we revisit the
masses, decay constants and the mixing parameters of the light pseudoscalar
mesons $\pi, K, \eta$ and $\eta'$. The low energy constants up to
next-to-next-to-leading order are determined by including the light-quark mass
dependences of the various quantities from different lattice QCD simulations
and relevant phenomenological inputs. Then we study the finite-temperature
behaviors of the masses of the light pseudoscalar mesons. The thermal behaviors
of the $\eta$-$\eta'$ mixing angles in singlet-octet and quark-flavor bases are
also explored. While the masses of the $\pi, K$, and $\eta$ are increased when
increasing the temperatures, the mass of the $\eta'$ turns out to be slightly
decreased in the low-temperature region.
