Which thermodynamic process takes place at a constant temperature so that the internal energy of a system remains unchanged?

Isothermal process is a change of a system, in which the temperature remains constant: ΔT = 0. So, if the thermodynamic process takes place at a constant temperature so that the internal energy of a system remains unchanged than this process is isothermal. 
The Joule's second Law states that the internal energy of a fixed amount of an ideal gas depends only on its temperature. So, isothermal processes are of great interest for ideal gasses.