When a volume of air is compressed, its temperature

 "increases" .

       "When a volume of air is compressed, its temperature   increases   . " 

Note:  The volume for the ideal gas law:

      →   "  PV = nRT " ; 

                in which:

                        "P = pressure" ; 
                        "V = volume " ; 
                        "n = number of moles of the gas" ; 
                       " R = the "ideal gas law constant" ; 
                       " T = temperature" .

   When a volume of air is compressed, the "pressure, "P", increases.

When the pressure, "P", on the "left-hand side" of the equation, increases, what effect does this have on the temperature, "T", on the "right-hand side" of the equation, all other factors held equal?    When the pressure, "P", increases, the temperature, "T", increases.

Note of interest:  This is how a "pressure cooker" works.