Final answer:
Adding heat to a system changes its internal energy but does not always lead to an increase in temperature, especially during phase changes like the melting of ice, where the energy goes into breaking molecular bonds. Similarly, doing work on a system can change the internal energy without heat transfer.
Step-by-step explanation:
Adding heat to a system indeed changes its internal energy, but it does not necessarily result in a temperature increase. An example of this can be observed during the phase change of a substance, such as the melting of ice. In this process, the added heat energy is utilized to break molecular bonds rather than to increase the temperature, hence the internal energy increases but the temperature remains constant.
Furthermore, when considering what happens to a system when heat is added, it's worth noting that the increase in internal energy may result in a change in pressure and volume, though the exact changes depend on the conditions of the process—highlighting that under different constraints (such as constant volume or pressure), the outcomes can vary.