You might not be getting any response because your definition of energy is vague..
If your talking about energy in the molecular kinetics form, temperature is always proportional to the average kinetic energy of the molecules of an ideal gas. (I'm also assuming your talking about gas because you mentioned adiabatic processes)
Other than that there are many forms of energy that have nothing to do with temperature.
E=MC^2 for mass-energy conversion is arguably a pretty common one that is not related to temperature.