  The transverse momentum ($p_T$) spectra from heavy-ion collisions at
intermediate momenta are described by non-extensive statistical models.
Assuming a fixed relative variance of the temperature fluctuating event by
event or alternatively a fixed mean multiplicity in a negative binomial
distribution (NBD), two different linear relations emerge between the
temperature, $T$, and the Tsallis parameter $q-1$. Our results qualitatively
agree with that of G.~Wilk. Furthermore we revisit the "Soft+Hard" model,
proposed recently by G.~G.~Barnaf\"oldi \textit{et.al.}, by a $T$-independent
average $p_T^2$ assumption. Finally we compare results with those predicted by
another deformed distribution, using Kaniadakis' $\kappa$ parametrization.
