Pretty straightforward question.
I'm fairly certain that it does make it hotter, but I'm not sure why. Is it conduction, convection, or what?
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The rate at which heat enters the box depends on the temperature difference between the inside and outside of the box.
The heat transfer through the box will be via conduction and radiation.
So you have to decide whether sitting on the box reduces or increases the outside temperature or is the temperature the same as before.
I would imagine that the temperature on the outside would increase and so the rate of flow of heat into the box will increase.