  Plutonium-based compounds establish an ideal platform for exploring the
interplay between long-standing itinerant-localized 5$f$ states and strongly
correlated electronic states. In this paper, we exhaustively investigate the
correlated 5$f$ electronic states of PuSn$_3$ dependence on temperature by
means of a combination of the density functional theory and the embedded
dynamical mean-field theory. It is found that the spectral weight of narrow
5$f$ band grows significantly and remarkable quasiparticle multiplets appear
around the Fermi level at low temperature. A striking $c-f$ hybridization and
prominent valence state fluctuations indicate the advent of coherence and
itinerancy of 5$f$ states. It is predicted that a 5$f$ localized to itinerant
crossover is induced by temperature accompanied by the change in Fermi surface
topology. Therefore itinerant 5$f$ states are inclined to take in active
chemical bonding, suppressing the formation of local magnetic moment of Pu
atoms, which partly elucidates the intrinsic feature of paramagnetic ground
state of PuSn$_3$. Furthermore, the 5$f$ electronic correlations are orbital
selective manifested themselves in differentiated band renormalizations and
electron effective masses. Consequently, the convincing results remain crucial
to our understanding of plutonium-based compounds and promote ongoing research.
