As the mother of a child who would NOT take her bottles cold, or room temperature, or any other way besides what we call "coffee hot" (she has some sensory issues) I can tell you that the bottle warmers at the Baby Care stations in both the MK and Epcot do work with Avent bottles. I never had to warm a bottle in the other parks, so I can't speak for them.
To be honest though, I usually used the microwave at the baby care centers to warm her bottles. I KNOW you're not supposed to, but the bottle warmers took forever to get the bottles as warm as she took them!
So, if you're comfortable microwaving them (at least the water), you have that option as well.