Heterodyne receivers for applications in astronomy need quantum limited sensitivity. We have investigated phonon- cooled NbN hot electron bolometric mixers in the frequency range from 0.7 THz to 5.2 THz. The devices were 3.5 nm thin films with an in-plane dimension of 1.7 X 0.2 micrometers 2 integrated in a complementary logarithmic spiral antenna. The best measured DSB receiver noise temperatures are 1300 K (0.7 THz), 2000 K (1.4 THz), 2100 K (1.6 THz), 2600 K (2.5 THz), 4000 K (3.1 THz), 5600 K (4.3 THz), and 8800 K (5.2 THz). The sensitivity fluctuation, the long term stability, and the antenna pattern were measured. The results demonstrate that this mixer is very well suited for GREAT, the German heterodyne receiver for SOFIA.