Why do you think there is a potential problem? When you mention the HMS vessels' cooling issues, what ships are you talking about? QE carrier and Daring class? Their problem with cooling is related to their architecture of IEP. Not the few degrees higher sea temperature.
A conventional GT will loose some percentage of power in hot climate, but not cripple anything. However that drop of GT power will mess up the load balancing and frequency synchronization (AC) of electrical power grid if not compensated and regulated instantaneously, eventually burning some components. The UK's IEP architecture failed to address this scenario adequately even though some engineers have anticipated this scenario but was ignored by the defense ministry.
It was not just that. The engine was supposed to have a Northrop Grumman (US) manufacture heat recuperator to increase efficiency, from what I understand, and it failed miserably at high temperatures. It did not have graceful shutdown or bypass or whatever.