Got the car back. It had a issue with the relay of the wiring of the fan which cools the radiator.
First they thought that it was the radiator and they changed that - it didn't work out. Then they thought it was a head gasket issue - but it was not that either.
Then they found out that there was an issue with the fan.
Khair, they did not charge for any of that - that's very kind of them
They also did a thorough check of the car and changed the oil and oil filter. They say the rest is fine
total bill: 120 pounds, which isn't too bad to get a 14 year old car which has been sparingly used fully checked up and tuned