BMW Mystery??? 2001 BMW 325i

I have a BMW 2001 325i with 210K.  The other morning, my Trans warning
icon came on when I went into DRIVE.  I slowly drove the car to a local
mechanic.  He said there was a leak in the cooling system and Tranmission
fluid had leaked and mixed with the coolant system.

He reco a new Radiator and some hoses ... and adding new T fluid as well.

I went to pick up the car to take it home to ponder this.

When I drove the car home .. the T warning icon DID NOT go on ... the car
drove OK ... A week later, I started the car and it was still OK.

If his diagnosis was right, I don't see how the car could be running OK
again .. when we did not do anything.

Confused?

Advice on where to go from here to get to the bottom of this without
spending a lot of money.