  The quark mass function $\Sigma(p)$ in QCD is revisited, using a gluon
propagator in the form $1/(k^2 + m_g^2)$ plus $2\mu^2/ (k^2 + m_g^2)^2$, where
the second (IR) term gives linear confinement for $m_g = 0$ in the
instantaneous limit, $\mu$ being another scale. To find $\Sigma(p)$ we propose
a new (differential) form of the Dyson-Schwinger Equation (DSE) for
$\Sigma(p)$, based on an infinitesimal $subtractive$ Renormalization via a
differential operator which $lowers$ the degree of divergence in integration on
the RHS, by $TWO$ units. This warrants $\Sigma(p-k)\approx \Sigma(p)$ in the
integrand since its $k$-dependence is no longer sensitive to the principal term
$(p-k)^2$ in the quark propagator. The simplified DSE (which incorporates WT
identity in the Landau gauge) is satisfied for large $p^2$ by $\Sigma(p)$ =
$\Sigma(0)/(1 + \beta p^2)$, except for Log factors. The limit $p^2 =0$
determines $\Sigma_0$.A third limit $p^2 = -m_0^2$ defines the $dynamical$ mass
$m_0$ via $\Sigma(im_0) = + m_0$. After two checks ($f_\pi = 93\pm 1 MeV $ and
$ <q{\bar q}>$= $(280 \pm 5 MeV)^3$), for $1.5<\beta<2$ with $\Sigma_0=300
MeV$, the T- dependent DSE is used in the real time formalism to determine the
"critical" index $\gamma= 1/3$ analytically, with the IR term partly serving
for the $H$ field. We find $T_c = 180 \pm 20 MeV$ and check the vanishing of
$f_\pi$ and $<q{\bar q}>$ at $T_c$. PACS: 24.85.+p; 12.38.Lg; 12.38.Aw.
