What would happen if I tempered aluminum of aeronautical use (Al 2024)?

2024 is precipitation hardened, meaning it is first solution treated to remove any precipitates already present and then quenched to stop more forming during cooling. Afterwards it is aged to reform the precipitates in a controlled manner.

As the solution treatment effectively gives you a fresh start repeating the whole cycle will give you the correct temper. But you will get some grain growth every time you do the solution treatment, which normally reduces the tensile strength slightly (not sure how much with 2024).

If you were thinking of just doing the aging stage (similar to tempering hardened steels), then the precipitates will already be present and it won't have much of an effect.

If it is not in the solution annealed condition , aging ( I guess that is what you mean by tempering) will do about nothing. If is in "as rolled" condition it may have cooled quickly enough to be partly solution annealed; then it may harden slightly during aging.