Huntsville Hospital's Heart Center and Heart Institute. Additional Phone Numbers (256) 801-6912 - Billing and Insurance (256) 265-7143 - Cardiac Rehab (256) 265-3012 - Coumadin Clinic (256) 265-6566 - Heart Failure Clinic (256) 801-6734 - Medical Records (256) 801-6851 - Prescription Refills The voice mail will ask a series of six questions..