  A thermal model, based on the Tsallis distribution and blast-wave model, is
proposed to compute hadron double-differential spectra $d^{2}N/dp_{T}dy$ in
$pp$ (also high energy $p\overline{p}$) collisions. It successfully describes
the available experimental data on pion and quarkonia ($\phi$, $J/\psi$,
$\psi(2S)$, $\Upsilon$ family) production at energies from $\sqrt{s} = 5$ GeV
to the LHC ones. Simple parametrizations for the $\sqrt{s}$ dependence of the
model parameters are provided allowing predictions for the yields of these
particles at new collision energies. The model can be used also for the pion
Bose-Einstein correlation studies.
