You shouldn't have a temp split on a new a/c from the factory as one engine, at the least, is always trimmed to give matching ITTs, not sure if this is just a williams policy?
To increase your n2 you need to burn more fuel thus higher ITT. If you need a higher N2 to achieve the same N1 there are a number of possible causes, dirty damaged fan/IP rotor or fan stator, a compressor bleed leak, and or a gas loss after the HPTurbine such as excessive LPturbine tip clearence.
A stuck bleed valve, anti-ice valve or leak is easily found on the 525 series. Give your engineering dept a call. A bleed leak in the tailcone could cause significant damage so if your concerned give them a shout.