  A universal form is suggested for the leading low temperature ($T$) behaviour
of the quenched free energy, $F_Q$, of various JT gravity and JT supergravity
theories once non-perturbative physics has been taken into account:
$F_Q{=}aE_{\rm gap}{-}b T^2/E_{\rm gap}{+}\cdots$, where $a$ and $b$ are pure
numbers of order unity. The non-perturbative scale $E_{\rm gap}{\sim}{\rm
e}^{-\#S_0}$, where $S_0$ is the black hole extremal entropy, is the average
value of the first non-zero energy level of the system. The quadratic part
confirms an earlier suggestion in the literature. The results come from
exploring a formula, proposed recently by Okuyama, for computing the quenched
free energy of a random system in terms of the connected correlators of its
partition function. It is combined here with results from non-perturbative
matrix model definitions of various JT gravity and JT supergravity theories,
using a combination of analytical and numerical techniques. Wormhole geometries
play a crucial role. Every currently available non-perturbative model of JT
gravity and JT supergravity is shown to confirm the formula.
