The purpose of this study is to determine whether a Penguin cold cap (used to reduce hair loss in patients with breast and ovarian cancers receiving chemotherapy) may also be effective at reducing hair loss in patients with multiple myeloma who are undergoing a stem cell transplant. Patients usually lose nearly all of their scalp hair after undergoing chemotherapy and stem cell transplantation for multiple myeloma. For many, the hair loss is upsetting and has kept some people from choosing to receive this potentially life-sustaining procedure. Melphalan is the chemotherapy drug used to kill the multiple myeloma cells prior to the stem cell transplantation. It kills cells that grow and replicate quickly (like hair cells). It is hoped that a cooling of the scalp will reduce injury to hair follicles. This may work because blood vessels in the skin constrict when cold, and this should reduce the amount of blood (and therefore melphalan within the blood) from getting to the hair follicles during the time of scalp cooling when the chemotherapy is in the body.