  We consider the BCS energy gap $\Xi(T)$ (essentially given by $\Xi(T) \approx
\Delta(T, \sqrt\mu)$, the BCS order parameter) at all temperatures $0 \le T \le
T_c$ up to the critical one, $T_c$, and show that, in the limit of weak
coupling, the ratio $\Xi(T)/T_c$ is given by a universal function of the
relative temperature $T/T_c$. On the one hand, this recovers a recent result by
Langmann and Triola (Phys. Rev. B 108.10 (2023)) on three-dimensional $s$-wave
superconductors for temperatures bounded uniformly away from $T_c$. On the
other hand, our result lifts these restrictions, as we consider arbitrary
spatial dimensions $d \in \{1,2,3\}$, discuss superconductors with non-zero
angular momentum (primarily in two dimensions), and treat the perhaps
physically most interesting (due to the occurrence of the superconducting phase
transition) regime of temperatures close to $T_c$.
