Sounds like the plant is not getting enough water. Bananas are greedy in terms of the watering and fertilizing needs. How often are you watering it? and How large is the container compared to the plant? Should be watering it every day at the temperatures you are providing. Also, very important, some soils (especially those high in peat moss), do not readily retain water. You may think you are watering, but the soil just beneath the surface may be bone dry. When you water, be sure to saturate the soil thoroughly. Also, consider transplanting to a larger container--bananas need their space--even the dwarfs.

My plant does this too when its in the direct sunlight. If I put it back on the porch out of the sun it looks green and healthy again. It gets watered with the rest of the flowers in the front yard every day. This is my second plant, the first one died because the company sent it in the middle of winter with no instructions...I want to make sure this one makes it.