I don't want to correct you like this but I am going too.
240º is not anywhere close to the fan turn on temps. If we want to get technical with real data the values are 212º low speed and 226º high speed. These are based on the 97-03 body style, the 2004-2008 cars are almost the exact same, within a few degrees of each other.
As said, hook up a scan tool and watch what that says. The cluster may be reading way different than the computer. If that is the case I'd break down a purchase a new OEM temp sensor, install a new thremostat at the same time and bleed the cooling system. Then see where you stand with the problem.
