The rudder is used to control the ship, so any form of disruption around it will affect the ships handling. A cage around the rudder, even if the pipes were space 1m apart, is likely to increase the ships turning circle and reduce its effectiveness in combat.
A solution to this would be to have the pipes formed to the shape of the rudder, effectively increasing its size and mass, or to replace the rudder entirely with one made of silver-coated bronze and have the pipes flow through it. The increased mass will make it harder to turn the rudder, so some form of assisted or power steering would be appropriate. If you're using a sailing ship (based on your other question I assume you are) then the ship already uses a pulley system to turn the rudder, you could just increase the number of pulleys to reduce the force needed to turn the wheel (although increasing the number of turns the wheel would need to make).
The difficulty with having the pipes turn is connecting them to the ship. A couple of solutions are available. 1 is to use a hose-like material if available, this allows the pipes to rotate and contract / expand freely. 308
The other option is to use a ball joint, for a rudder that just turns from one direction to the other this should be sufficient, though may limit the maximum turning angle of the rudder.
If you were to heat up the pipes, thus heating the rudder this would only have a minor effect on the surrounding water, but it would reduce turning efficiency a bit. Warmer water would produce less flow over the rudder, reducing the force being imparted by the water. As the water passed over the warm rudder it heats up. But as long as the ship is moving, the warm water is constantly being replaced with cold water, so the effect would only be minimal, perhaps even negligible. The bigger problem I think would be keeping the rudder warm. You'd need to be constantly pumping hot water through the rudder to combat the cooling effects of the sea water. 108