Down the sides. The exhaust can hide it from view. They’d have to be really bad to drop noticeable warm water though.

Heat exchanger/oil cooler at the back of the engine maybe. I had to replace mine.

Run your motors with your boat on the trailer with drives down at a launch when it’s not busy… if that’s an option. This will allow you to bring your rpms up and not be dependent on the hose. Another if…put it in gear and put a load on the motor IF you’re not going to destroy the launch. Back in just far enough for your water pickups so your boat doesn’t end up in the back of your tow rig if you do put it in gear.