It would be helpful to know what your configuration is and what cooler you're asking about.
Some of our machines pass freshwater through the interstage coolers and jacket using a small circulation pump - then pass the freshwater through a cooler that's fed with seawater from the ship's firemain.
Leaks of air into the freshwater system tend to make the header tank overflow and overheat the cylinders (which causes a loss in delivery pressure on a good day, discharge overtemp trips on the sort of bad day when you're lucky and complete collapse of outlet pressure accompanied by rapid unscheduled disassembly if you're unlucky and the cooling is somehow accidentally restored suddenly).
If you've got a FW/SW cooler and that leaks, the most likely effect is ingress of seawater into the FW system. Big leaks will be detectable quickly as the header tank overflows. Small leaks are more insidious, and your headache is going to be internal corrosion (which will eventually make the machine run hotter, but will take it's time to get there).
A.