Your copper tubing is acting as a heat sink for the exhaust - which is probably about the temperature of hot water (since the engine is water cooled). But that is not "hot" in terms of neoprene of plastic. Being copper, the tubes readily transmit heat to your fingers (or anything else - copper being a super conductor) which is why they feel so warm/hot.

If the tubing were made out of plastic, it would not get as hot to touch.

A couple items to check with your system:

1. With the heat, and the difference in metals, there electrylysis/corrosion. You might be better served using aluminum tubing.

2. Is the seal where the tubing meets the lower unit ssolid. You might want to use some sort of sealant to be sure that no exhaust is leaking around the stuck tubes.