  In this research, we present an alternative methodology to search for
ring-like structures in the sky with unusually large temperature gradients,
namely Hawking points (HP), in the Cosmic Microwave Background (CMB), which are
possible observational effects associated with Conformal Cyclic Cosmology
(CCC). To assess the performance of our method, we constructed an artificial
data set of HP, according to CCC, and we were able to retrieve $95 \%$ of
ring-like anomalies from it. Furthermore, we scanned the \textit{Planck} CMB
sky map and compared it to simulations according to $\Lambda CDM$, where we
applied robust statistical tests to assess the existence of HP. Even though no
significant ring-like structures were observed, we report the largest excess of
HP candidates found at $\alpha = $1\% significance level for the analyzed sky
maps (CMB at 70GHz, SEVEM, SMICA, and Commander-Ruler), and we stress the need
to continue the theoretical and experimental research in this direction.
