Excellent point. I just checked their website and from what I am reading, even in bulk sizes, it should come in an 'airtight container'. A bag in a box would not qualify. I would definitely call them.
Plastic certainly can be an air-tight container. I have used vacuum-sealed plastic bags for packaging food, and other things for many years. The vacuum sealer sucks the air right out and no air gets into the container until I cut it open.
I hate to expose it to any heat because it's just in a plastic bag and I don't want leakage.
As far as leakage of oils when it starts to soften, I have not had that happen. My recent order of palm shortening, which is hydrogenated palm and does not need to be stirred, came in plastic inside a box. The plastic my oils come in is really quite thick and sturdy. I generally get my oils from Soapers Choice, so can't really speak to what plastic WSP uses, but i doubt their packaging is significantly different. And I can also vouch for WSP's very responsive customer service.
If your home is as cool as mine, it could take a few days for the palm to soften up, but if you are really concerned it could leak as it softens, put an extra layer of protection underneath it (a tarp or a large heavy ply garbage bag, for example) while it sits in your kitchen (if you were able to get it as far as your kitchen.) I suspect your kitchen is the warmest room in your house most of the time, and the floor is likely easy to clean, so that's a good location for it to sit. An area rug underneath will provide a bit of insulation if the floor has too much cold air underneath (like when you have a cold cellar below the kitchen).
Another thing you can do to facilitate gentle, yet faster softening, is to put a space heater in the room. As the ambient air heats up, the palm oil will eventually start to soften. Oh, and for now, keep the top of the box open to let in more heat. Cardboard insulates, so it's going to keep the cold inside the box longer than if the plastic encased palm were completely exposed to the warmer air.