You need to figure out how many volumes of CO2 you need. If you carb at higher temperatures, you need a higher pressure to introduce the volume into the beer. When you cool the keg you vent your headspace and then set your regulator for the new pressure. This should keep your carbonation constant.
For example, if you wanted to carb your Pilsner to 2.5 volumes (I think that's around what a Pilsner needs) at 57ºF, you would have to put it on at 21psi for a week or so. When you cool the keg down to about 40ºF you would have the same volume at only 12psi. Purge the headspace and put your regulator on at 12 psi just as you cool the keg.
BTW, you should put your location in your profile so we Canucks can recognize each other. There are starting to be quite a few of us here.