Abstract The study investigates the suitability of friction heating, generated by the forming tool rotation, to form polymer sheets during single-point incremental forming, and the possibility to control the temperature of the sheet by the selection of proper processing parameters. Polycarbonate sheets were formed to produce a square pyramid frustum geometry, varying the tool rotation speed and the traveling speed and monitoring the temperature. Load measurements were performed during the process, as well as the evaluation of the surface roughness and the elastic springback, to determine the influence of these processing conditions. Moreover, a thermo-mechanical numerical model was developed to understand the main phenomena involved. The results confirmed that the processing temperature, which increases with the tool rotation speed and decreases with the traveling speed, influences the sheet forming process and can be controlled by the selection of the processing speeds. A phenomenological model of the heat exchange was introduced to better explain the temperature evolution during the process and how it is influenced by the processing speeds.