The overall efficiency of the Penning-trap mass spectrometer SHIPTRAP at GSI Darmstadt, employed for high-precision mass measurements of exotic nuclei in the mass region above fermium, is presently mostly limited by the stopping and extraction of fusion-evaporation products in the SHIPTRAP gas cell. To overcome this limitation a second-generation gas cell with increased stopping volume was designed. In addition, its operation at cryogenic temperatures leads to a higher gas density at a given pressure and an improved cleanliness of the helium buffer gas. Here, the results of experiments with a 219Rn recoil ion source are presented. An extraction efficiency of 74(3)% was obtained, a significant increase compared to the extraction efficiency of 30% of the present gas stopping cell operated at room temperature. The optimization of electric fields and other operating parameters at room as well as cryogenic temperatures is described in detail. Furthermore, the extraction time of 219Rn ions was determined for several operating parameters.