I would imagine that any rubbermaid bin will be made from Polyethylene or Polystyrene. Both of which have melting points of about 220 F... and if you can get a human heating pad that high... well we won't need to even think of a consequence because it's not possible. Conclusion: no melted plastic from a heating pad! and unless you're trying to heat it in a pool of lighter fluid or gasoline, I doubt you'll be starting any fires either (actually I'd bet that both of those would evaporate before they could ignite from the heat you could put off with a heating pad).
BTW I'm a material sciences major (senior in college), so material properties are kinda my thing, however if you still don't feel secure using it, you could always do a check on a bin you buy (usually the recycling code on the bottom will give you enough info to determine the type of plastic it is, or the very least narrow it down to a couple types) and then wikipedia the melting point.