A random temporal graph is an Erdős-Rényi random graph $G(n,p)$, together with a random ordering of its edges. A path in the graph is called increasing if the edges on the path appear in increasing order. A set $S$ of vertices forms a temporal clique if for all $u,v \in S$, there is an increasing path from $u$ to $v$. Becker, Casteigts, Crescenzi, Kodric, Renken, Raskin and Zamaraev [(2023) Giant components in random temporal graphs. arXiv,2205.14888] proved that if $p=c\log n/n$ for $c\gt 1$, then, with high probability, there is a temporal clique of size $n-o(n)$. On the other hand, for $c\lt 1$, with high probability, the largest temporal clique is of size $o(n)$. In this note, we improve the latter bound by showing that, for $c\lt 1$, the largest temporal clique is of constant size with high probability.