  A \emph{random temporal graph} is an Erd\H{o}s-R\'enyi random graph $G(n,p)$,
together with a random ordering of its edges. A path in the graph is called
\emph{increasing} if the edges on the path appear in increasing order. A set
$S$ of vertices forms a \emph{temporal clique} if for all $u,v \in S$, there is
an increasing path from $u$ to $v$. \cite{Becker2023} proved that if $p=c\log
n/n$ for $c>1$, then, with high probability, there is a temporal clique of size
$n-o(n)$. On the other hand, for $c<1$, with high probability, the largest
temporal clique is of size $o(n)$. In this note we improve the latter bound by
showing that, for $c<1$, the largest temporal clique is of \emph{constant} size
with high probability.
