  We study the latent heat and the pressure gap between the hot and cold phases
at the first-order transition temperature $T=T_c$ of SU(3) Yang-Mills theory,
using the small flow-time expansion (SF$t$X) method based on the gradient flow.
We first examine alternative procedures in the SFtX method -- the order of the
continuum and vanishing flow-time extrapolations. We confirm that the final
results adopting the two orders, as well as other alternatives in which the
perturbative order of the matching coefficients and the renormalization scale
of the flow scheme are varied, are all consistent with each other. We also
confirm $\Delta p$ is consistent with zero, as expected from the dynamical
balance of two phases at $T_c$. For the latent heat in the continuum limit, we
find $\Delta \epsilon /T^4 = 1.117(40)$ for the spatial volume $L^3$
corresponding to the aspect ratio $N_s/N_t=T_cL=8$ and $1.349(38)$ for
$N_s/N_t=6$. From hysteresis curves, we show that the entropy density in the
hot phase is sensitive to the spatial volume, while that in the confined phase
is insensitive.
