MAX cold psi means exactly that..that is the most you should inflate the tire to when COLD , it takes into account what tire pressure will be when it warms up
For example , The tires on my WRX said "max cold psi 44" which I did. Next day it was 70+ degrees and when I checked them they were about 55 psi......
As long as you don't exceed the max cold psi rating , the tire should be fine.....
A few years ago I worked at a gas station ..... had a guy come in one day , complaining that his car was riding VERY hard..... said he'd put air in his tires a few weeks before , but since he did not have an air guage , he had to guess by how "hard" the tire felt....
When I check his tires , a couple of them were over 100 psi
And this was on a Honda....:smoker2: :smoker2: