Does temperature of water affect carbonation process For sake of the question:

I'm using a Sodastream brand
I like max carbonation
Normally, I use cold water from my Brita pitcher out of the refrigerator

Sodastream's FAQ states:

However, we do recommend using COLD water to achieve best results.

I suspect that best results means max carbonation, and I should use cold water. Or a conspiracy theorist could suggest their lawyers promote cold water so fewer machines will blow up. Or maybe it has something to do with flavor..
Anyway, just curious about this. I don't have the physics pedigree to know the answer.
Carbon Dioxide (and gases in general) dissolve more easily in cold liquids. This means that it's easier to carbonate (inject with Carbon Dioxide) your soda using cold water than warm. As your liquid heats up the gas falls out of solution creating the bubbles in your soda. Fountain dispensers usually have the water lines run through the ice hopper (or they have a cold plate) to further chill the cold water they feed to the machines for this same reason.