I co-wrote an article in the American/Canadian ALPA magazine about this very topic. I was also on the team that wrote the FAA directive for implementation of cold temp techniques.
The formula that was used was the old true altitude formula, and in most cases that will still be correct, but there has been a new formula developed. The new formula appears in ICAO PANS-OPS VI, I worked closely with the Canadian officials here and ICAO in Montreal about it's implementation. So I guess one could say that this subject is close to me. I also developed a training course that I used for some in the U.S. Also, I wrote a program that does corrections automatically. Hope this info helps, any more questions, just ask...