Considering that temperature is related to how agitated are the particles of a material and that there is a limit of how fast something can move (speed of light); doesn't it imposes an upper limit on the temperature?
That is a somewhat simplified definition of temperature. While there's a parallel discussion on the same topic at [0], the term you're looking for is Planck temperature [1]. There is no "upper cap" on temperature per se, but we also don't have any models for describing what would happen beyond that point. See [2] for more discussion.
I mean, replacing v_rms by c in equation 3 in https://chem.libretexts.org/Bookshelves/Physical_and_Theoret... gives us an upper limit for the temperature of a gas, right?