Air carrier Dispatcher reported the Captain initiated a call to discuss a passenger's portable refrigeration device in use on the aircraft and plugged into the AC power outlet. After discussion and research it was determined the unit should be unplugged and the passenger provided with ice to keep the medical contents sufficiently cool.

Narrative

At approximately XA20Z the Captain initiated a call to discuss a passenger with a personal; portable refrigeration device in use on the aircraft and plugged into the AC power outlet. The only reference that could be found was in the FOM . This only referenced whether or not an item was allowed on the aircraft and did not address what to do with the item on the aircraft. Customer service was notified and I was referred to discussing the matter with an customer service manager. Customer service was notified and I was tasked with finding the make/model of the device (Torronbe; CB01); its contents; etc. I asked the Captain to have the device unplugged from AC power. A Flight Attendant gave the passenger some ice to keep the medicine inside the cooler at an acceptable temperature. After relaying this information to the Customer Service Manager who discussed the matter with operations control; I was informed that it was TSA-Approved to use a refrigeration device with insulin. medicine; etc for personal use. The only reference for this in our company manual was under 'MEDICAL EQUIPMENT AND SUPPLIES'. This guidance references 'Liquid or gel low blood sugar treatment including juice'; 'Insulin dispensing products; jet injectors; pens; infusers; and an unlimited number of unused syringes; when accompanied by insulin Lancets'; 'blood glucose meters; blood glucose meter test strips';. 'insulin pumps; and insulin pump supplies' with no mention of refrigeration devices. The Dangerous Goods Manual makes no mention of guidance for 'refrigeration machines' other than they are allowed in checked bags and not in carry-on bags. No information or manual for this model device that could provide possible battery size; wattage; mechanical operations; etc was found on the internet. The Captain and I decided to continue to ZZZ1 and briefly discussed enroute airports that would be acceptable alternates should any issue arise from the device before ending the call.Information on what to do when a prohibited item is on the aircraft would be helpful.