A unit (1, 1) for sterilizing a web (2) of packaging material for a machine for packaging pourable food products, the unit (1, 1) having a sterilizing chamber (3) containing a liquid sterilizing agent at a first temperature (T 1 ) conveying means (9a, 9b, 9c) for feeding the web (2) through the sterilizing chamber (3) before the web is formed into a succession of sealed packages of pourable food products a hold tank (11) for the sterilizing agent feed means (13, 15, 16, 12) activated selectively to feed the sterilizing agent from the tank (11) to the sterilizing chamber (3) drain means (12, 17, 18) activated selectively to drain the sterilizing agent from the sterilizing chamber (3) into the tank (11) in the event of stoppage of the packaging machine and cooling means (55 55) activated selectively, at the end of the package production cycle, to cool the sterilizing agent in the tank (11) to a second temperature (T 2 ) lower than the first temperature (T 1 ) . ( Figure 1 )