The complexity in this thread is making my head spin.
My Leaf-powered Mini has a small coolant loop, and the pump failed months ago. I didn't even notice. The only time temps ever got over 60°C was when I was literally running up a mountain in the summer. My batteries don't get warm to the touch unless the cells are under 3.7V.
Granted, this is an 1800lb car, and the Leaf batteries don't get any of the coolant running through them, but I'm not light on the throttle, and it gets hot in Los Angeles. I would be very surprised if the stock radiator of an ICE car couldn't easily handle the heat output of an electric motor and its batteries for street driving. Like when my pump was working, I was using a Prius inverter radiator. Now the water isn't even forcibly flowing and it's okay.
I would run a single loop with a single pump and a single radiator: tank -> pump -> batteries -> inverter -> motor -> radiator (or really, whatever layout is simplest). If it proves inadequate, add complexity.
Batteries get hot from high-speed charging, and inverter/motors get hot from long high-speed runs (like minutes/hours on a highway). What am I ignorant of? Under what scenarios are other conversions overheating where mine is not?
PS - Getting rid of heater cores is one of the best things about ditching internal combustion...Heated seats go a long way, and a supplemental HV heater/defroster will take care of the rest...rapidly.