A multistage compressor includes a first compression stage and a second compression stage connected in series with the first compression stage that receives and further compresses gas from the first stage. A first cooling element is connected between the first compression stage and the second compression stage. A second cooling element is connected to a discharge of the second compression stage. The multistage compressor further includes a cooling unit for providing cooling airflow to the first and second cooling elements. The cooling unit includes a fan and a first temperature sensor that determines a temperature of gas discharged from the first cooling element. The cooling unit is configured to increase or decrease a fan speed based on a temperature determined by the first temperature sensor. A method of controlling fan speed of a cooling fan of a compressor is also provided.