Gosh, all the way from Kansas City?! (hee hee) I think the answer is no. There used to be an outside service that rented mini-refrigerators to Disney guests. Disney put a stop to that a year or so ago. I want you to know, however, that all is not lost as you may be able to rent one at your WDW resort. Here is the webpage, for example, for the
Grand Floridian Resort :
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Guest Rooms:
These rooms feature two queen-size beds, one day bed, table and chairs, ceiling fan, vanity area with two sinks, and bath. Most Guest Rooms offer private balcony. Many Guest Rooms feature garden or water views. Non-smoking rooms and rooms for Guests with disabilities are available.
Guest Room amenities include in-room safe, voice mail, phone in bath area, robes, hair dryer, iron and ironing board, and minibar. A limited number of refrigerators and microwaves are available on request.
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Many of the resorts have mini-refrigerators for rent. Please check with your resort (a phone call to your resort's Front Desk should give you your answer).