  We report highly sensitive specific heat measurement on mesoscopic
superconducting loops at low temperature. These mesoscopic systems exhibit
thermal properties significantly different from that of the bulk materials. The
measurement is performed on a silicon membrane sensor where 450 000
superconducting aluminium loops are deposited through electron beam lithography
under an applied magnetic field. Each entry of a vortex is associated to a jump
in the specific heat of few thousands of Boltzmann constant kB indicating the
existence of phase transitions. The periodicity of this sequential phase
transitions is a nontrivial behaviour and varies strongly as the temperature is
decreased. The successive phase transitions are well described by the
Ginzburg-Landau theory of superconductivity. The presence of metastable states
is responsible for the n-&#61510;0 (n=1, 2, 3...) periodicity of the
discontinuities of the measured specific heat.
