According to my findings, you are absolutely correct in your assumption the regulation will be different according to Temprature, and altitude! Not as much by altitude as temprature, however!

I have two different regulateing loads for the doubles I use in the North American winter hunting at high altitude, say 4000 ft above sea level, up, and 20 to 60 deg temp fahrenheit , which takes in most of the western USA. Another load for the same rifle to be used in Africa, at sea level to 1500 ft above sea level, and in 90 to 120 deg fahrenheit heat. The loads are worked up for each sittuation either at my sister's home in PHX Arizona, @110 degs, or at my home in the Dallas/Fort Worth area in winter, @ 400 ft above.

Neither of these loads will regulate at it's opposite condition, very well. I find most Britt rifle regulate pritty well with factory at between 30, and 70 degs and under 1500 ft above, but have to use the tropical load in Africa, from September through November! For this reason, amoung others, I choose to hunt Africa in late June, to 15 Aug, when the temp in most of Zimbabwe, Zambia, and Caprevi are between 35 degs at night, to a high of 70 degs in the day, both temps fahrenheit !

Please note the change from centigrade to fahrenheit !