In thermodynamics we talk about an adiabatic process where the heat or mass or substances are NOT transferred between a thermodymanic system and its environment. This does not mean that the temperature is constant.
Once is set that the heat is not added into the system, and knowing that the First law of thermodynamics says that:
The change in internal energy is equal to the heat added into the system minus the work done BY the system itself. (ΔU = Q – W)
Therefore, the change in the energy in the system is in the work done.