In this paper, results of preparatory tests for a space experiment “Marangoni in Films” on board International Space Station are reported. The setup is thermalized at a setpoint temperature so that (thermal) Marangoni convection is exclusively a result of evaporative cooling of the film, here composed of a Hydrofluoroether (HFE)-7100, evaporating into nitrogen at a given setpoint pressure. The present paper is entirely devoted to the evaporation rates, whereas the Marangoni convection itself will be analyzed in future studies. Apart from the temperature and nitrogen pressure, various setpoints for the initial relative saturation in HFE-7100 vapor are explored. A special design of the test cell with a square chimney surrounding a square opening of the liquid layer permits to largely stabilize the evaporation rates during a longest-lasting middle stage (beyond the initial transients and the final film dry-out). In addition, it facilitates the use of vapor (digital-holographic) interferometry for measuring the evaporation rates, the results of which are compared with independent measurements by means of the pressure evolution within our sealed cell of a fixed volume. An excellent agreement is found before the final dry-out stage for all setpoint parameter combinations tested. The study is accompanied by numerical finite-element simulations in an axisymmetrized geometry, neglecting a possible influence of the Marangoni convection and verifying certain premises used in interferometric post-processing. Even if the simulation results might somewhat over-/underpredict in each particular case, the overall dependence of the evaporation rate on the setpoint parameters is well reproduced and the role of the buoyancy convection is thereby explored.