Can Polyethylene Dissolve on 50-60 °C I know that polyethylene's melting point is between 115–135 °C, however I would like to know if can it start dissolving between 50-60 °C? 

In a real example, if I put warm food (straight from the oven, I think it can be max. 50-60 °C) into a re-closable polyethylene plastic bag and close it, will any chemical reaction affect the food (from the polyethylene's side)? Or is polyethylene safe at that temperature, and if the bag is warm it doesn't mean that any chemical reaction is started? I didn't experienced any alteration, but I'm not an expert and don't know much about chemistry yet, so I would appreciate some guidance.
There may be better answers forthcoming, but a chemical does not need to melt (i.e. be in the liquid phase) to be reactive. For example, your food very likely has some liquid component, and that could be enough to react with some solid. Now polyethylene is used all over the place and is very nonreactive in many non-rigorous situations (like food service), so you are probably just fine. But I wanted to make the more general point that you don't have to be a liquid or gas to be reactive.