  In this study we measure physical parameters of the same set of 155 M and
X-class solar flares observed with AIA/SDO as analyzed in Paper I, by
performing a {\sl differential emission measure (DEM)} analysis to determine
the flare peak emission measure $EM_p$, peak temperature $T_p$, electron
density $n_p$, and thermal energy $E_{th}$, in addition to the spatial scales
$L$, areas $A$, and volumes $V$ measured in Paper I. The parameter ranges for M
and X-class flares are: $\log(EM_p)=47.0-50.5$, $T_p=5.0-17.8$ MK, $n_p=4
\times 10^9-9 \times 10^{11}$ cm$^{-3}$, and thermal energies of $E_{th}=1.6
\times 10^{28}-1.1 \times 10^{32}$ erg. We find that these parameters obey the
Rosner-Tucker-Vaiana (RTV) scaling law $T_p^2 \propto n_p L$ and $H \propto
T^{7/2} L^{-2}$ during the peak time $t_p$ of the flare density $n_p$, when
energy balance between the heating rate $H$ and the conductive and radiative
loss rates is achieved for a short instant, and thus enables the applicability
of the RTV scaling law. The application of the RTV scaling law predicts
powerlaw distributions for all physical parameters, which we demonstrate with
numerical Monte-Carlo simulations as well as with analytical calculations. A
consequence of the RTV law is also that we can retrieve the size distribution
of heating rates, for which we find $N(H) \propto H^{-1.8}$, which is
consistent with the magnetic flux distribution $N(\Phi) \propto \Phi^{-1.85}$
observed by Parnell et al.(2009) and the heating flux scaling law $F_H \propto
H L \propto B/L$ of Schrijver et al.(2004). The fractal-diffusive
self-organized criticality model in conjunction with the RTV scaling law
reproduces the observed powerlaw distributions and their slopes for all
geometrical and physical parameters and can be used to predict the size
distributions for other flare datasets, instruments, and detection algorithms.
