To calculate the temperature increase of air when pressurized from atmospheric pressure to 3 bar using a piston-type air pump, one can apply principles from the adiabatic process. The relevant formula for an isentropic process is T2/T1 = (p2/p1)^(gamma-1/gamma), where gamma is 1.4 for air. The initial temperature T1 is typically the normal atmospheric temperature. The discussion emphasizes the importance of determining whether the process is isentropic or polytropic, as this affects the calculations. Understanding these principles is crucial for accurate temperature predictions during air compression.