Activation energy and temperature
The two distribution plots shown here are for a lower temperature $T_{1}$ and a higher temperature $T_{2}$. The area under each curve represents the total number of molecules whose energies fall within particular range. The shaded regions indicate the number of molecules which are sufficiently energetic to meet the requirements dictated by the two values of $E_{a}$ that are shown.

It is clear from these plots that the fraction of molecules whose kinetic energy exceeds the activation energy increases quite rapidly as the temperature is raised. This the reason that virtually all chemical reactions (and all elementary reactions) are more rapid at higher temperatures.

Activation energy seems to be more of a material or reaction pertinent . Say a reaction has $10J$ as $E_{a}$ to proceed but has $20 J$ kinetic energy - I would say the the additional energy is transferred/carried on by the products after reaction is complete. So having more K.E shouldn't affect the character of a reaction but only its kinetics .