Is wearing socks obligatory during prayer and in public, and is there an exception for cases of extreme heat sensitivity?

Previously, it was established that a woman must cover her feet during prayer or when going out if she fears they might be seen by a non-mahram (definition). Wearing socks is not a condition; rather, they can be covered by letting down her garment or by any other means. Therefore, covering the feet with socks is not obligatory, nor is it superior to covering them by other means if possible.