This is second time cooling fan keeps running on high speed after turning off the car, and the fan will not stop until I disconnected the negative battery terminal.

I replaced the Hi-speed fan relay as it was really hot.

Not disconnecting the battery will just keep the fan running until the battery is dead.

This is not normal as some cars keep the fan running for few minutes after the engine off under some conditions, but this is not designed to do that in case you are wondering.