No, the internal energy of a system will not necessarily increase if its temperature is increased.

Explanation

1. Internal energy is defined as the sum of the kinetic energy and potential energy of molecules of the system. It includes only the energy associated with the random motion of molecules of the system.

2. The important thing about internal energy is that it depends only on the state of the system, not how that state was achieved.

3. Thus, the internal energy of a given mass of gas depends on its state described by specifics values of pressure, volume, and temperature.

4. The internal energy of ideal gas depends on only on temperature.

5. For system other than ideal gas, internal energy depends on pressure, volume and temperature combined.