I folllow your argument. But to use colder water from the house
supply to circulate through the car radiator gizmo where will this
water go to? Certainly potable water is too precious to let it run to
waste or even to over water the lawn. A simpler and more effective
patch would be to put a block of ice infront of the fan.

OP claimed that his water was not metered, and there's apparently
enough of it so that he was considering dumping it on his roof,
to cool that off. (which he could still do, actually...)

Out of curiosity, does anyone know if a vortex-tube
will work on water, or does it only work on gasses?