The hot water heater, using engine coolant as a heating medium, will tend to slow the heating of the coolant (and the engine) until the hot water reaches the same temperature as the thermostat setting. Whether the already heated hot water tank will cause the engine to run hotter is doubtful. (there has to be a temperature difference for heat transfer to occur)
The PO likely changed it out because it had started to corrode and fail. West Marine and others carry a range of heaters, choose a stainless one that fits in the space you have available. The better ones will cost more but last longer. Most will include an electrical element for heating water with shore power, as well as the plumbing to use engine coolant.