How did the Universe thermalize to the same temperature before inflation? Inflation is speculated to take place at about $10^{-35}$ seconds after BigBang. The idea is that at that moment the universe was small enough so that photons could thermalize to reach the same temperature. For the source see Our Baby Universe: Ed Copeland (6.30 minutes) Then that region underwent an exponential expansion. How does this argument fit with the fact that there were no photons at that time? 
 A: This is the timeline in the standard cosmological model:

There are no photons before the spontaneous weak symmetry breaking time, so there is no way they define an ensemble to have a temperature, which is a thermodynamic variable, i.e. the statistics of very many particles.
During the inflationary epoch, the inflaton field dominates , a theoretical model formed to reconcile the observations with the theory, and explain the cosmic microwave background radiation  (CMB)small inhomogeneities, but that background comes at the transparency point of light, 200.000 years or so after the Big Bang.

The idea is that at that moment the universe was small enough so that photons could thermalize to reach the same temperature.

It is not photons that homogenize the universe at inflation time, but inflatons, and the small inhomogeneities result in the small deviations of the CMB from the perfect uniformity, which explains galactic clusters and galaxies.
If you watch the timeline after photons appear , a bit before $10^{-10}sec$, they can start interacting with quarks and then with hydrogen and deuterium until the universe expands enough that the photons do not find scattering centers and mainly decouple, at the transparency time. This give a snapshot of that time,of  how matter was distributed. The $10^{-5}$ inhomogeneity seen in the CMB spectrum correlates with clusters of galaxies.
One has to spend some time studying  the models and the mathematics of the models.
