  The hot nucleus $^{171}$Yb is investigated by the covariant density
functional theory with the PC-PK1 effective interaction. The thermodynamic
quantities are evaluated with the canonical ensemble theory. The pairing
correlations is treated by the shell-model-like approach, in which the particle
numbers are conserved strictly and in which the blocking effect is handled
exactly. An S-shaped heat capacity versus temperature of $^{171}$Yb appears. It
has been studied in terms of the blocking effect, the single-particle levels,
the pairing gap, and defined seniority components, and compared to the heat
capacity of $^{172}$Yb. The pairing transition from the superfluid state to the
normal state can result in the S-shaped heat capacity of $^{172}$Yb where the
one-pair-broken and two-pair-broken states dominate, while the single-particle
level structure near the Fermi surface is associated with the S-shaped heat
capacity of $^{171}$Yb. For odd-A nuclei, although the one-pair-broken and
two-pair-broken states still contribute, the pairing gap and the pairing
transition is relatively weak. The S-shaped heat capacity could be affected due
to the blocking of the single-particle level near the Fermi surface.
