Can activation energy be changed by changing the temperature?
If you add a catalyst, that easily reduces the activation energy by changing the reaction mechanism to a more efficient one.
Beyond that, activation energy, the energy needed for a reaction to occur, by itself is nearly constant...
But if we were to be nitpicky, it still ever so slightly depends (inversely) on temperature at extraordinarily hot reaction conditions. The inverse dependence becomes greater in magnitude the more complex the molecules involved and the higher the temperature gets.
At high enough temperatures, certain molecules, particularly polyatomic three-dimensional ones, can access so-called "high-lying vibrational states", meaning they can vibrate in more ways and store more energy in these motions.
This adds a little to the average kinetic energy of the ensemble of molecules, and could potentially lead to a slightly lower activation energy at sufficiently high temperatures (i.e. THOUSANDS of kelvins!).
But again, this is rather slight, and can be ignored.