Estimates of the bombarding energies necessary to reach the quark-gluon phase in heavy-ion collisions are presented within a hydrodynamical framework. At intermediate energies (3-7 GeV/nucleon) the quark-gluon matter formed is predicted to be rather cool (below 100 MeV), i.e. much colder than nuclear matter without phase transitions. Further, the consequences of first-order phase transitions from the neutron matter to pion-condensed matter and quark matter are discussed for neutron stars. Quark matter does not fulfil the conditions for the existence of a third stable branch, e.g. stars with quark cores. Because of observational constraints on neutron-star masses, pion condensation is restricted to a narrow first-order phase transition at best. Due to this restriction the rapid growth of a pion-condensed core in a neutron star cannot appear as a supernova-like event as suggested in earlier work.