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Herschel is an ESA scientific satellite with a cryogenic payload for astronomical infrared observations, to be launched in 2007. The thermal control system of the Herschel Extended Payload Module (EPLM) shall provide a 1.65 K heat sink for 3.5 years mission lifetime. The major parts of the EPLM are the Cryostat Vacuum Vessel (CVV), the Herschel Solar Array and Sunshade (HSS) and the 3.5 m Telescope. The CVV contains a 2367 ❘ superfluid Helium tank and the Optical Bench, which carries the three scientific instruments. The CVV also carries the Telescope and the Local Oscillator Unit (LOU) used for one scientific instrument. Furthermore, the CVV is equipped with external radiators and internal vapour-cooled shields. The EPLM is mounted on top of the Herschel Service Module (SVM). In addition, a thermal shield is arranged between SVM and CVV. This paper describes the EPLM thermal design and the main thermal analysis results for operation on ground and in orbit.