Since cold fermentation usualy takes like 24 hours or longer, the dough temp is a "non issue". It does not matter if you cool it down to 6 degrees celcius starting from 28 degrees or 26 degrees. It will take a few extra minutes to cool fully cool down but on the 24 hours, that does not matter. As soon as the temperature is the same throughout the whole dough, the fermentation and rise will do it everywhere the same. Also when bringing it up to temp again, you are not doing that in 5 minutes time. You need a much longer time for that so it will go very gradualy so you will not see (a lot of / any) difference in the outside or inside.
So the dough temperature "only" applies to same day dough. I did a search if I could find some sites talking about it. Here is some theory wich I think explains it. http://www.weekendbakery.com/posts/a-few-tips-on-dough-temperature/
Short story. Optimum is just over 27 celcius / 80 Fahrenheit. At 21C/70F the activity of the yeast has roughly halved, so the fermentation will take twice as long.
21C/70F is roughly room temperature. Imagine me kneeding a big loaf of bread. Recipy says let it rise for 45 minutes. I kneed it and my dough temperature is 27 degrees when I start my rise. 45 minutes later, the outside of my dough ball has cooled down to 21 degrees. The inside will have a higher temperature. Since 6 degrees Celsius 10 Fahrenheit apperantly makes a 100% difference (or 50% depending on where you start to count) that will have a big impact on my final result.
How about if your room temperature at your house is 19 degrees.... A few degrees here and there can make a big difference on your final product. Especialy for OP since he wants to produce the same results every time. So I do think temperature matters. If you (can) control all the variables, it will be easier to produce consistent results.