EMIR is a wide-field camera and a multi-object, intermediate resolution near-infrared spectrograph for the GTC telescope. EMIR is a cryogenic instrument whose cooling system is based on four two-stage CCCs' Leybold Coolpower 5/100 whose cooling capacity is 100W@80K, in the 1st stage, and 5W@20K, in the 2nd stage, operated directly by two compressors in dual mode (two cold heads for each compressor). During the verification phase some phenomena affecting the cooling system efficiency have been observed. In consequence, the possible influences of the temperature of the water in the cooling unit the compressor, the compressor input power and the quality of the insulating vacuum in the instrument have been studied. Contamination in the Closed Helium Cycle is another possible cause that has been evaluated. The methods used in the tests and the cleaning procedures are described. The results allow us to reach some conclusions regarding the use and maintenance of this type of cooling systems.