I am about half way through my paper on "Internal Cooling of Exhaust Valves in IC Engines". I managed to get hold of some wartime tests in which water was flowed through an exhaust valve of a big American radial engine. The heat input was quite high, more than 3kW, into a few square inches.Valve temperatures droped from over 700 to less than 200 deg C.
I then used this data to assess some First World War tests by the RAE, who partially filled a valve stem with water, and used what is now called the "thermosyphon" effect to transfer heat from the valve crown to the top of the stem. Calculations also suggest very high heat transfer rates. I suspect that the high accelerations and decelerations, resulting from the reciprocating motion of the valves, affected the boundary layers, and this helped... Quite possibly the condensation heat transfer rate could have approached droplet rates.