GRAVITY is a 2nd generation VLTI Instrument o which operates on 6 interferometric baselines by using all 4 Unit Telescopes. It will deliver narrow angle astrometry with 10μas accuracy at the infrared K-band. At the 1. Physikalische Institut of the University of Cologne, which is part of the international GRAVITY consortium, two spectrometers, one for the sciene object, and one for the fringe tracking object, have been designed, manufactured and tested. These spectrometers are two individual devices, each with own housing and interfaces. For a minimized thermal background, the spectrometers are actively cooled down to an operating temperature of 80K in the ambient temperature environment of the Beam Combiner Instrument (BCI) cryostat. The outer casings are mounted thermal isolated to the base plate by glass fiber reinforced plastic (GRP) stands, copper cooling structures conduct the cold inside the spectrometers where it is routed to components via Cu cooling stripes. The spectrometers are covered with shells made of multi insulation foil. There will be shown and compared 3 cooling installations: setups in the Cologne test dewar, in the BCI dewar and in a mock-up cad model. There are some striking differences between the setup in the 2 different dewars. In the Cologne Test dewar the spectrometers are connected to the coldplate (80K); a Cu cooling structure and the thermal isolating GRP stands are bolted to the coldplate. In the BCI dewer Cu cooling structure is connected to the bottom of the nitrogen tank (80K), the GRP stands are bolted to the base plate (240K). The period of time during the cooldown process will be analyzed.