Hi "FireFire"!

I think you'll "pay through the nose" for a room with a refrigerator near Barajas airport. Too bad you're not staying at
Hostal Adriano/Adriá near the Puerta del Sol as they have refrigerators in all rooms.
Barring a refrigerator and while I know nothing about it, you might consider the
Hostal Los 5 Pinos . It's probably quite bit cheaper than the typical corporate & expensive hotels near Barajas airport. It's still more expensive than most other hostels ("hostales") but cheap for those around the Madrid airport.
UPDATE: After re-visiting their website, all rooms at the
Hostal Los 5 Pinos have a MINIBAR so I suppose you could use that as your refrigerator.
They write:
The Hotel Has a total of sixty double rooms. All they are equipped with a bathroom, telephone, minibar, safebox, musical thread, coffeshop, independent aconditioned air and free private parking.
Good luck! Saludos, MadridMan
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