I use the cat5 to distribute ethernet throughout. This was before wifi was any good, and I still use the cat5 all day every day. Gigabit is not supposed to work with cat5, but it does just fine.
I hadn't thought of the on demand heater. But it's hard to beat a $10 microwave that just plugs in.
Try it some time. You'll never go back to cold washcloths!