  The Q-Star structures, also called as gray holes with a radius of two times
greater than the corresponding Schwarzschild radius of same mass and from the
compact neutron star family with a very high density, have been obtained by
using a generalization of $q$-deformed fermions with two parameters $q$ and $p$
as the constituents of the star. Because the interaction between particles are
controlled by deformation parameters in $q,p$-fermions instead of a complicated
interaction Lagrangian, we consider the deformation parameters giving the
maximum Q-Star pressure between the interacting particles of stars. The cold
and hot Q-Stars in temperatures of $T=0$, $T=40\ \mathrm{MeV}$ and $T=60\
\mathrm{MeV}$ have been investigated from the numerical solutions of TOV
equations and it is obtained that the Q-Stars can reach up to $13$ solar mass
and $75$ Km radius. Moreover, it is found that the total mass and radius of the
star increase when the star gets cool down, and a much denser state is reached.
