The answer to this question is that the number of molecules with sufficient energy to react increases. The lack of reactivity at room temperature is not due to lack of collision. Since high temperatures favor fast rate of reactions, energy in a given molecule determines whether the molecule will react.
At some temperature, some molecules react and some molecules do not react. There must be a continuous distribution of energy between the molecules.
As the system temperature rises, the average energy in the system also increases. The
increase in reaction rate due to temperature increase is mainly due to
an increase in the number of molecules with sufficient energy to react,
not an increase in the number of collisions.
