Burning can be good or bad. If the feeling is a wave of warmth, as if you just put Ben-Gay on your forearms, then it is good. That means that you really are relaxed, and you're getting a soothing sensation. However, if your muscles are burning from fatigue, and you feel like you can't play more, then it's obviously bad. If it was the good kind of burn, then you would feel energized, not hindered.
I would agree in part with faulty damper in that you may be using too much of your fingers. After all, your fingers have no muscles, they are actually moved by the muscles in your forearms. Therefore, if you are using your fingers too much, the first place you would feel it is in your forearms.
Without being able to see you play it, this is what I would suggest:
Play the piece slowly at a speed where you can comfortably play the piece with complete accuracy, control, and relaxation. Then practice breathing. It may sound ridiculous, but breathing is a problem that many pianists don't even think about. Lack of oxygen leads to much quicker muscle fatique, and practicing regular breathing when you're playing will always aid your relaxtion tenfold. Like I said, just play the piece at a comfortable speed, and practice breathing deep breaths at regular intervals through your nose (breathing through your mouth excites the heart and counteracts the relaxation aspect). You may find at first that concentrating on breathing will screw up your playing a little bit, and that's probably your first sign that you aren't breathing enough. It's definitely possible that you may be having another problem, but I promise you that if you practice breathing you will notice a difference in your playing. It will make you much more fluid and relaxed.