Answer: Based on your description I am not certain what is happening to your rabbits foot fern. The warmth and higher humidity outside might help it to recover. Make sure it is in a very shady spot.
Normal room temperatures between about 65 and 80 degrees would be fine. This plant needs high humidity to do well, so perhaps the air conditioning is drying out the air (or perhaps it is in a cold draft.) You could set it near a sink or put it on a pebble and water tray to help humidify the air around it. This is a shallow tray filled with pebbles and water added to just below the top of the pebbles. Set the plant pot on the pebbles so the bottom of the pot is just above the water. Top up the water as needed to replace what evaporates.
It does best in medium to bright but indirect light such as through a north window. Too much sun could cause it to dry out.
The soil should be kept evenly moist like a wrung out sponge, not sopping wet and not dried out. Overwatering or underwatering could cause root damage and cause the foliage to die back.
This plant is also sensitive to overfertilizing. Use a water soluble fertilizer such as 10-10-10 plus minors but dilute it to about one fourth the rate on the label directions.
Finally, this fern normally grows its rhizomes all over the outside of its container. It does not need repotting until it becomes difficult to keep the soil evenly moist. At that time, you may have to break the pot to release it. You can start new plants using bits of healthy rhizome. If you think you may lose this one, you could try that as "insurance."
I hope this helps you trouble shoot.
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