Activation energy has a term that is proportional to temperature according to transition state theory (at least). For instance, for the bimolecular reaction A+ B --> P, we have E$_{a}$=$\Delta^{\ddagger}H^{\ominus}$+nRT where $\Delta^{\ddagger}H^{\ominus}$ is standard enthalpy of activation, n=2 for gas reaction and 1 for reaction in solution. This said, for many reactions, the activation enthalpy is much larger than RT (which is ~2.5 kJ/mol at 300K) and the activation energy can be approximately regarded as temperature independent.
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