Reviewing and adding.....
Hot water heaters opperate 2 or 3 different ways, depending on the model of the hot water heater.
1) 110V from shore power or generator (may also use 12v for electronic support)
2) propane to heat the water and 12v for electronic support
3) from the main vehicle engine, anti-freeze running through the hot water heater
We special ordered a 2007-2350. The 2007 brochure stated a 3-way hot water heater, but we got a 2-way. I never did question that, though I should have. Now years later, I am glad I have a 2-way hot water heater for mechanical simplicity. Having heater hoses from the V10 engine running back there would be a plumbing mess.
On our trips, we rarely have shore power and minimally run the generator, so we don't have hot water available all the time. We usually heat the water with propane, sometimes when driving. So far no issues from the heater's exhaust.