Is the Energy Associated with the Loss or Gain of Information Dependent on Temperature?

I believe it was Leo Szilard who derived a relationship between entropy and information:
/S = k ln(2) where k is Boltzmann’s constant and /S is the change in entropy of a bit of information. If each side is multiplied by the temperature, T, we calculate an energy.

So, is the energy of a gain or loss of information dependent on temperature?

My interest relates to information horizons such as the edge of the observable universe, and the CMB.