Preparation of black formamidinium lead iodide (FAPbI3) requires high temperature annealing and the incorporation of smaller A-site cations, such as methylammonium (MA+), cesium or rubidium. A major advantage of vacuum processing is the possibility to deposit perovskite films at room temperature (RT), without any annealing step. Here we demonstrate stabilization of the cubic perovskite phase at RT, in a three-sources co-sublimation method. We found that the MA+ incorporation is a self-limiting process, where the amount of MA+ which is incorporated in the perovskite is essentially unvaried with increasing MAI deposition rate. In this way a phase-pure, cubic perovskite with a bandgap of 1.53 eV can be obtained at room temperature. When used in fully vacuum-processed perovskite solar cells, PCEs up to 18.8% were obtained. Despite the presence of MA+, the solar cells were found to be thermally stable and maintained 90% of their initial efficiency after 1 month of continuous operation.