If you have forced air heat make sure it is not in the line of fire. By that I mean make sure that the vent is not blowing at the palm or in its directions.
Forced air heat is the worst for drying up plants. I have not had forced air heat in years but I remember killing a lot of plants because they were near heating vents.
My mom use to keep her heat up to 80 so it was so hot in her house I had to wear summer cloths when I had to sit in her house more than 10 minutes. It was truly hot and tropical at her house in the winter.
