In my experience, many funeral homes do not have a refrigeration unit. It is too costly. Usually the orthodox jewish funeral homes do have them due to their religious beliefs, no embalming and burial before sundown.
But in all honestly, it has been reported that there is not any soft connective tissue left, therefore, really no reason to embalm. The body can be treated with external embalming solutions and/or powders. There would be no need for a refrigerator at this point. The body could stay out at room temp in a cardboard box or on a table until services. At that point she would be place in a small body bag and either cremated or buried in a casket.