The Pathfinder version of Mending does not specify if it works on burnt items, merely saying that it does not work on items that have been "warped or otherwise transmuted", which may, or may not apply to burnt items, depending on interpretation. As Ilmari Karonen points out, it also requires that "All of the pieces of an object must be present", something which I would assume would be the case if the note's only been in the fire for a round, but may not be. Lastly, as Matthew Najmon points out, repairing the piece of paper to full hp and functionality doesn't necessarily restore the ink and message. This is a cantrip, and your party will likely have access to it. http://www.d20pfsrd.com/magic/all-spells/m/mending
Make Whole, while quite powerful, has nothing to say it's better at repairing burnt items than Mending, nor does it remove the requisites of requiring all of the pieces, nor does it necessarily restore the message if the paper is repaired. http://www.d20pfsrd.com/magic/all-spells/m/make-whole
If your party kills the villain, Speak with Dead will allow a will save, but if the villain's corpse fails the will save, then it is obliged to answer questions truthfully. While it can give vague or cryptic answers to questions, there are no real vague or cryptic answers to the question "What was the exact wording on the note written on this piece of paper?", and they'll get a couple of tries (two, perhaps three). Speak with Dead is a 3rd level spell, and while your party may not be able to cast it, if they have access to a medium sized city, they can drag the corpse around and hire somebody else to.http://www.d20pfsrd.com/magic/all-spells/s/speak-with-dead
Obviously, the easiest answer is to capture the villain alive, and get them to tell the party what the note said, using social skills such as intimidate, Bluff, etc, or mind effecting magic such as charm person or suggestion.