Water engine pump killing 12v battery

You likely have an engine temp sensor going bad or a relay sticking or a loose connection somewhere in that system.
My guess is that you need a shop visit.
Hopefully it will be a fairly simple fix for someone with the right information to know where to look.

 

If the water pump in Gen 4 is like the one in Gen 3, this post (and following) will explain how it is controlled.

There is one wire that supplies the pump with +12 volt power, and another that tells the pump how fast to run. The "how fast" signal is generated by the ECM as a train of pulses, where the more time spent high, the faster the pump runs.

The pulse train is generated by the ECM pulling down while the pump itself pulls up. So if that circuit is open somewhere or the connection is bad, the pump will see that as a "run as fast as possible" signal.

That still leaves the question of how the pump has power to run at all. In Gen 3, the circuit that brings it +12 V power is controlled by a relay and would be off when the car is off. A look in the Gen 4 wiring diagram (more info) would clear up whether that is different in Gen 4 / indicate what else to check.