Radiator fan loud and does not shut off with engine off

Radiator fan sounds like a jet engine, out of the blue, and stays on after ignition is off. Have to pull fuse to make it stop. Replace fuse after a cool down and fan is off. Does not come back on until engine temperature warms up.
Tried two new relays, disconnected negative battery cable. Still occurring. Ordered a resistor, will change that tomorrow, then possibly a coolant sensor? I do not understand the correlation between super loud and not shutting off? Seems like two different issues to me. Any help would be appreciated.