  In this paper, an improved multi-source thermal model is used to analyze the
transverse momentum spectra in $pp$ collisions at high energies ranging from
$\sqrt{\mathrm{\it s_{NN}}}$ = 62.4 GeV to 7 TeV. We give a detailed comparison
between the theoretical results and experimental data at RHIC and LHC energies.
It is shown that the excitation factors of emission sources depend linearly on
ln$\sqrt{\mathrm{\it s_{NN}}}$ in the framework. Based on the variation
regularity of the source-excitation factors, transverse momentum spectra are
predicted in $pp$ collisions at higher energies, potential future $pp$
colliders operating at $\sqrt{\mathrm{\it s_{NN}}}$ = 33 and 100 TeV.
