Do not worry about Hazel being cold. She will be fine. If you make sure she's eating quality calories to provide body heat, she won't get cold. At night, she will huddle closely to her pals and get heated that way, too.
How old is Hazel? You say she's been molting for months but started a few weeks ago. You need to clarify that.
If she is older than eighteen months, and if she began molt in fall and it was incomplete, then she would probably pick it up again to finish. Sometimes, molt can be postponed or...