Here are my thoughts.
Take a microwavable container that will hold your bean bag and then you can use the food court microwave without worrying about germs. You can also bring sanitizer wipes for the microwave in the food court. You can opt for a preferred location near the food court for an additional charge per night and then, you would have it more convenient to do this for your son. Preferred rooms are in high demand; so, I'm not sure how easy it will be for you to change your reservation.
Is there anything else that might work like a warm washcloth from the sink in your resort room? What about an electric warmer that you could bring? I agree a heating pad might work. A hot water bottle can be wrapped with a towel and perhaps work for your son. I'm not sure the tap water from your room will be hot enough for a water bottle, but there is hot water available in the food court for tea.
If you are driving down bring your own microwave. We bring medical equipment with us on trips.
It will cost you, but you could take a taxi and buy a cheap microwave down there. You could perhaps order one from the Internet and get it delivered to your resort. Many get a food and water order delivered to their resort for pick up once they get there.
You might be able to change your Disney resort to a room which includes a microwave. If you change from a value to a deluxe it will be a costly upgrade.
Stay off site where you have a microwave. Some off site resorts have transportation back and forth to the parks. This transportation is not as good as Disney's service. You could rent a car.
Call special needs guest services and see what can be done.