A calorimeter box is made up of Copper because
i) Cu has low SHC & thus it reaches the equilibrium temperature quickly by absorbing a small amount of heat.
ii) Cu is highly malleable & hence a very thin box of small mass can be made thus decreasing the heat capacity of the box. This makes sure calorimeter absorbs or liberates a small amount of heat during the heat exchange.
iii) Cu is a good conductor of heat.