A particle beam apparatus has a cooled anti-contaminator (18) and/or a cooled specimen holder (17). A thermal conductor (19) is provided for providing a connection between the anti-contaminator (18) and/or the specimen holder (17), on the one hand, and the cooler (21) of a cryogen vessel (20) on the other hand. The thermal conductor (19) includes a carbon fiber bundle. With the carbon fiber bundle (19a, 19b), a high thermal conductivity is ensured between the cooler (21) and the surface (17, 18) to be cooled. At the same time, thermal expansions are avoided which lead to a displacement of the anti-contaminator (18) and/or the specimen holder (17).