The internal energy is a function of the state variables for the system.
The concept of internal energy and its relationship to temperature.
Since the internal energy is a function of both temperature and pressure, it's difficult to give an answer to your question.
The driving force for heat transfer is temperature, not internal energy.
What can be measured, however, is the change in internal energy of a system.
Today one instead discusses the internal energy of a system.
So we can only talk about the "change" in internal energy.
For an open system, internal energy can be changed also by transfer of matter.
The increase in internal energy makes the temperature go up.
Indeed the processes of life depend on this internal energy.