A quick look at my camera. I don't see anywhere that could hold any amount of grease. In fact I would be surprised if there is anything other than a light coat of silicone grease anywhere on the camera. What material was used to pack the camera? Bubble wrap? If so it should have melted as well. Are the plastic parts inside the camera damaged? If not the outside was exposed to heat.
I suspect the camera was too close to a heat source after unpacking. Perhaps on the kitchen counter next to the stove. Or it might have been used for some other purpose.