  Di Pietro and Komargodski have recently demonstrated a four-dimensional
counterpart of Cardy's formula, which gives the leading high-temperature
($\beta\rightarrow{0}$) behavior of supersymmetric partition functions
$Z^{SUSY}(\beta)$. Focusing on superconformal theories, we elaborate on the
subleading contributions to their formula when applied to free chiral and U(1)
vector multiplets. In particular, we see that the high-temperature expansion of
$\ln Z^{SUSY}(\beta)$ terminates at order $\beta^0$. We also demonstrate how
their formula must be modified when applied to SU($N$) toric quiver gauge
theories in the planar ($N\rightarrow\infty$) limit. Our method for
regularizing the one-loop determinants of chiral and vector multiplets helps to
clarify the relation between the 4d $\mathcal{N} = 1$ superconformal index and
its corresponding supersymmetric partition function obtained by
path-integration.
