A unit for sterilizing a web of packaging material for a machine for packaging pourable food products includes a sterilizing chamber containing a liquid sterilizing agent at a first temperature a conveying device for feeding the web through the sterilizing chamber before the web is formed into a succession of sealed packages of pourable food products a hold tank for the sterilizing agent a feed mechanism activated selectively to feed the sterilizing agent from the tank to the sterilizing chamber a drain activated selectively to drain the sterilizing agent from the sterilizing chamber into the tank in the event of stoppage of the packaging machine and a cooling device activated selectively, at the end of the package production cycle, to cool the sterilizing agent in the tank to a second temperature lower than the first temperature.