Are any jet engines used in combat aircraft water cooled? Are any jet engines used in combat aircraft water cooled?

If they are not, and instead are air cooled, how can the engine ensure consistent cooling? Wouldn't the airflow passing through whatever radiator implementation it has be greatly affected by the airspeed? Consider low subsonic numbers with heavy maneuvering in a dogfight, vs. mach 2 sustained flight?

While I can imagine that variable air inlet for the radiator would change the airflow, I really have no idea how this would work.

I'm also aware that certain rocket engines, e.g. the F-1 allow the fuel itself to circle around the thrust chamber to cool it. Perhaps a similar system is used in jet engines.
Jet engines are cooled and temperature managed by the mass air flow itself which is used to surround and limit the boundaries of the flame, keeping it away from the burner can walls, and dilute the heat of the flame as it passes to the turbine (only a minority of the mass airflow's oxygen is actually burned - which is why afterburners work; there's lots of leftover oxygen to work with). 

If you're talking about using a closed liquid cooling system with heat exchangers taking heat from the burner can and turbine somehow, well, I've never heard of a water jacketed burner can, and how you could use liquid in a closed system to cool a turbine, who knows.  

Liquid cooling was used in the past as supplemental cooling to increase available power by spraying water directly into the mass flow as mentioned here, but in that case the water is a consumable.