Can You Solve this Ice Diamond Riddle? ft. Vsauce’s Michael Stevens

Here's good physics "riddle". Or if you prefer, a question from an engineering exam in Heat Transfer...

You have two  boxes , lined with a black coating, which contains an object with identical starting energy (heat). You can assume that the inside surface temperature of these two boxes are the same. Assume that this box is a closed system with Identical initial conditions.

One of these boxes is on earth and the other is inside a spaceship. The spaceship is pressurized to replicate the atmospheric conditions on earth (pressure/composition/etc...). There is no significant gravity on this spaceship.

The question: Will these two objects lose energy at the same rate? If not, which one will cool down faster and why?