Without ensuring high productivity, single-point incremental forming allows obtaining cavities in sheet-type workpieces by rotating and moving a rotary forming tool along a predetermined path. The process can be used in the case of both metal and plastic sheets. The heat generated in the processing area is expected to cause different elongations and contractions, affecting the final dimensional accuracy of the surfaces obtained. A full factorial experiment with three independent variables at two levels was used to investigate the correlations between the values of some of the process input factors and the results of thermal processes developed at the contact between the rotating tool and the workpiece. Experimental research was performed in dry single-point incremental forming, using lubricants and, respectively, with the generation of a decrease in temperature by the use of coolants. Empirical mathematical models were determined, and they confirmed the influence of the values of considered input factors on the thermal processes developed at the contact between the tool and the workpiece material. Temperatures of up to 147 °C were recorded in the processing area of the plastic workpiece.