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. Barnaföldi et.al., by a T -independent average p 2 T assumption. Finally we compare results with those predicted by another deformed distribution, using Kaniadakis' κ parametrization.