The use of cooling air during machining is an environmentally conscious procedure, and its applicability to different processes is a research priority. We studied tapping operations, an important operation in the assembly process, using cooling air with unreinforced polyamide (PA66) and polyamide reinforced with glass fiber (PA66-GF30). These materials are widely used in industry, but their behavior with respect to tapping has not been studied. We analyze the outcomes regarding the thrust force, torque, and power at cutting speeds between 15 and 60 m/min. The experimental tests were executed using cooling air at 22 °C, 2 °C, and −18 °C in dry conditions. The M12 × 1.75 mm taps were high-speed steel, with cobalt as the base material and coatings of TiN and AlCrN. To identify the more influential factors, an analysis of variance was performed, along with multi-response optimization to identify the desirability values. This optimization shows that the optimum for PA66can be found in environments close to 3 °C, while the optimum for PA66-GF30 is found at the minimal temperature studied (−18 °C). Thus, cooling air can be considered an adequate procedure for tapping operations, to increase the sustainability of the manufacturing processes.