Neurologist Dr Michael Watt apologised to a barrister after he accused the former patient of wasting his time and "reaching your own diagnosis".
The barrister claimed he had been advised by the senior consultant to take "cold showers after exercise".
This, he was told, would help manage his exercise-induced migraine, which Dr Watt had incorrectly diagnosed.
After the consultation with Dr Watt in October 2011, the QC wrote a letter of complaint to the senior consultant neurologist about his diagnosis and advice.
In a letter seen by this newspaper, Dr Watt said the former patient's attitude was "hard to understand" and accused him of "reaching your own diagnosis".
The patient also complained to the General Medical Council (GMC) in December 2011.
He said: "I felt he was not fit to practise medicine and I copied his letter and gave a description of the consultation.
"The GMC accepted that and began a preliminary process.
"Dr Watt was invited to write an explanation and he did so in January 2012.
"He's quite contrite in the letter, but he at no stage explained how he got that diagnosis or treatment plan."
Dr Watt told the GMC that he had "never written such a letter before and will never again" and apologised for the manner of his reply.
The patient - who does not want to be named - added: "The GMC decided not to proceed any further with any in-depth investigation. There was no hearing, no evidence, no fitness to practise aspect.
"I was disappointed by that as I felt very strongly that he was unfit to practice and I said that to the GMC.
"I told the GMC that I did my duty, that they have a responsibility to patients and my fear was this man was going to cause injury or worse to patients in the future."