I have only kegged one batch of beer, so I am not an expert here. But I think the following is how CO2 pressure works.
The goal is to get a certain volume of CO2 into our beer. Say for example 2.01 volumes. That can be achieved at different temperatures, using different PSI.
We could achieve a volume of 2.01 CO2 by force carbonating in a keg at 35F using 5 PSI.
We could achieve a volume of 2.01 CO2 by force carbonating in a keg at 40F using 7 PSI.
We could achieve a volume of 2.01 CO2 by force carbonating in a keg at 45F using 9 PSI.
See the following chart: http://www.kegerators.com/carbonation-table.php
So if your beer has a CO2 volume of 2.01, then it's PSI will be lower at lower temperatures, and higher at higher temperatures. But the volume of CO2 should be the same.
Use a carbonation chart, or the BeerSmith carbonation tool to help set the desired volume of CO2.
This is my understanding on CO2. If I have any of this incorrect, then please let me know. I hope this helps.