Ah, sorry - when I say engine temp, I mean actual engine temp (listed in WT as Oil Temp), not exhaust temp (listed in WT as Engine for jets). Part of the Water Injection System are sprayers on the compressor stages to reduce engine temps. Additionally the main oil cooler in the AV8’s is a fuel-to-oil cooler, so higher fuel flow in turn helps to keep oil temps under control.
Having said that I’m still fairly certain that JPT should fall during water injection, even though the maximum permissible JPT is higher, as the system is also used to increase the allowable intake air temp at which full thrust can be maintained by +15C.