  Using ALMA data, we have studied the HC$_3$N and continuum emission in the
starburst ring (SB ring) and the circumnuclear disc (CND) of the SB/AGN
composite galaxy NGC 1068. We have detected emission from vibrationally excited
HC$_3$N (HC$_3$N*) only towards one star-forming region of the SB ring.
Remarkably, HC$_3$N* was not detected towards the CND despite its large HC$_3$N
$v=0$ column density. From LTE and non-LTE modelling of HC$_3$N*, we obtained a
dust temperature of $ T_\text{dust} \sim 250$ K and a density of
$n_{\text{H}_2}=6\times10^5$ cm$^{-3}$ for this star-forming region. The
estimated IR luminosity of $5.8\times10^8$ L$_\odot$ is typical of proto-Super
Star Clusters (proto-SSC) observed in the SB galaxy NGC 253. We use the
continuum emissions at $147$ GHz and $350$ GHz, along with CO and Pa $\alpha$,
to estimate the ages of other $14$ SSCs in the SB ring. We find the youngest
SSCs to be associated with the region connecting the nuclear bar with the SB
ring, supporting the scenario of sequential star formation. For the CND, our
analysis yields $T_\text{dust} \leqslant 100$ K and
$n_{\text{H}_2}\sim(3-6)\times10^5$cm$^{-3}$. The very different dust
temperatures found for the CND and the proto-SSC indicates that, while the dust
in the proto-SSC is being efficiently heated from the inside by the radiation
from massive proto-stars, the CND is being heated externally by the AGN, which
in the IR optically thin case can only heat the dust to $56$ K. We discuss the
implications of the non-detection of HC$_3$N* near the luminous AGN in NGC 1068
on the interpretation of the HC$_3$N* emission observed in the SB/AGN composite
galaxies NGC 4418 and Arp 220.
