  By applying the particle-number projection to the finite-temperature BCS
theory, the $S$-shaped heat capacity, which has recently been claimed to be a
fingerprint of the superfluid-to-normal phase transition in nuclei, is
reexamined. It is found that the particle-number (or number-parity) projection
gives $S$-shapes in the heat capacity of nuclei which look qualitatively
similar to the observed ones. These $S$-shapes are accounted for as effects of
the particle-number conservation on the quasiparticle excitations, and occur
even when we keep the superfluidity at all temperatures by assuming a constant
gap in the BCS theory. The present study illustrates significance of the
conservation laws in studying phase transitions of finite systems.
