The storage box that is used to escape the classroom would get hotter, not colder in the time it takes Don to collect it. It would take days for the residual heat to radiate away from the box assuming no other effects were in play. In this case though there are two other effects to consider. Firstly, as long as the passengers are breathing they are converting chemical energy into heat. Secondly and more importantly they are shown to be on the light side of the planet so would be receiving direct solar warming. As a comparison the temperature of the ISS outer hull is around 120 degrees centigrade when in sunlight.