Only sentence A is correct.

No. sentence B is clearly wrong. The "to" is unnecessary and out of place.

The right answer is that...neither of the two sentences are correct. In English, after the word "than", an "ing" form is required. So the right sentence is: "in modern society, clothes do more than just KEEPING us warm". When two dogs fight, a third gets the bone!

This is my opinion: Both A and B are correct. You could also correctly say: “In modern society, clothes do more than TO just keep us warm.” Perhaps B sounds a little weird, but that doesn’t necessarily make it incorrect. Whether or not something sounds weird is often a matter of personal preference. If Steven Larrabee can provide an argument for why B is incorrect I will accept it, of course. But so far he hasn’t really done that in my opinion, only stated that he doesn’t like it.

Now that i am ready it again, i think i would pick B.