In recent years the Loschmidt echo has created a lively debate about its connection to equilibrium and dynamical phase transitions as determined by the order parameter. In my talk I will discuss the proper generalization of the Loschmidt return rate to finite temperatures and apply it to fully connected spin models. For these mean-field type models, it is found, that return rate and order parameter produce the same phase diagram. By introducing a simple, geometric interpretation of the Loschmidt echo we are able to understand the underlying mechanism.