In the field of nuclear structure physics with in-beam gamma-ray spectroscopy one can identify three main lines of investigation: High spin states, states at a high temperature and states in nuclei far from stability. In future we hope to reach all three together. With H.I. fusion reactions it has been possible to achieve two of them together, namely the study of high spin states in nuclei far from stability. In this talk we report on the study of states at higher temperature. Before discussing this matter, we will briefly asses the reasons why we want to study states at higher temperatures in nuclei, that are states which lie by 1–2 MeV or even higher above the yrast-line. One reason is that we have very little knowledge about such states. There are only a few nuclei in which even the first three 0+, 2+ or 4+ levels are known. Yet significant tests of nuclear models such as e.g. the Interacting Boson Model [1,2], the Shell-Model or the Excited VAMPIR-Model  need states above the yrast line. A crucial test of nuclear models should not only consist in finding some of the predicted levels of this model but it must also confirm the absence of levels which are not predicted by the model. This brings the concept of complete spectroscopy into the discussion.
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