The technical data sheets of all manufacturers of duct tape stipulate the need for surface preparations along the lines of
All surfaces must be clean, dry and free of dust, grease and other loose material. Adhesion tests prior to application are recommended.
In other words, you tape the container while it’s still clean and dry.
The technical data sheets also typically give an application temperature
of up to or around +50°C; which is well above a human’s core temperature.
So the glue won’t get soft at the temperatures which are to be expected in the use case discussed.
As to the surface structure of the tape: in this particular case I would consider it to be a useful feature as it would help to keep the container in place.
