I use these bottles for many daycare babies (I do home childcare). I have 2 using them now..one a brestfed baby, one formula. I have never owned a bottle warmer aparatus.
For formula fed babies, I just use the right temp water that baby prefers when I mix it up. Currently my little one prefers on the warm side. For the breastfed guy, his mom sends frozen formula in the sealed bags, so I pull what I need out and have a container I put hot tap water in to thaw. As I putter in the kitchen I change out the water (takes me a minute, literally) until it is thawed and the right temp when I need it. I never microwave or whatever. I only use tap water and he likes it pretty much the hot side of warm! I have never had an issue.
I have never worked in a center, but they do have ratios that should make it possible for them to have the time to do such a simple thing as properly warm a bottle, without needing to resort to methods that melt it. Otherwise, I agree with the others and send it in a "regular" bottle, just with a cap lid on it to be used for warming and have your Playtex bottles all set up (if you send them?) with the drop-in bag inside, nipple and cap assembly on and a cover. Then they can simply pour the warmed milk inside. I supply all those elements (even formula..Mommy obviously provides the breastmilk =), so its easier for me (I dislike a diaper bag going back and forth each day...)
Good luck!