  It is challenging to build a model that can correctly and unifiedly account
for the deconfinement phase transition and thermodynamics of the hot $SU(N)$
pure Yang-Mills (PYM) system, for any $N$. In this article, we slightly
generalize the massive PYM model to the situation with a quasigluon mass
$M_g(T)$ varying with temperature, inspired by the quasigluon model. In such a
framework, we can acquire an effective potential for the temporal gauge field
background by perturbative calculation, rather than adding by hand. The
resulting potential works well to describe the behavior of the hot PYM system
for all $N$, via the single parameter $M_g(T)$. Moreover, under the assumption
of unified eigenvalue distribution, the $M_g(T)$ fitted by machine learning is
found to follow $N$-universality.
