  We present the first measurements of thermal signatures of the Little-Parks
effect using a highly sensitive nanocalorimeter. Small variations of the heat
capacity $C\_p$ of 2.5 millions of non interacting micrometer-sized
superconducting rings threaded by a magnetic flux $\Phi$ have been measured by
attojoule calorimetry. This non-invasive method allows the measurement of
thermodynamic properties -- and hence the probing of the energy levels -- of
nanosystems without perturbing them electrically. It is observed that $C\_p$ is
strongly influenced by the fluxoid quantization (Little-Parks effect) near the
critical temperature $T\_c$. The jump of $C\_p$ at the superconducting phase
transition is an oscillating function of $\Phi$ with a period $\Phi\_0=h/2e$,
the magnetic flux quantum, which is in agreement with the Ginzburg-Landau
theory of superconductivity.
