I don't think the box in that photo is complete or ready to work yet. I haven't seen that project before, but I can tell it's missing something. It needs vents, fans, louvers, or something to let the hot air escape.
When enclosing diodes in a protective box, you need to provide some way for the heat to get out, all the way out. Normally, the heat will be conducted to the heat-sinks, where it (a) radiates away and (b) convects the air. If the air is locked in a box then the convection loss is cut off. If the radiated energy is captured in the box, and then re-radiated from the warm box wall, half going out and half back inward then the box acts as an insulator, and keeps heat inside. That makes the diodes even hotter than they would be.
It's definitely wise to enclose diodes and the heat sink in something, especially if the heat sink becomes electrically active in the circuit. Safety demands at least that. But to enclose them without any way of letting the heat out will lead to trouble. If you want to re-use something more appropriate, I'd suggest using a box somewhat like a house fuse panel or circuit breaker panel, with lots of space inside, holes, and insulated tabs for mounting things. Knock-out a lot of the conduit holes from the sides of that box and there will be plenty of ways for air to circulate.
Another consideration is if it will be mounted outdoors or indoors. Obviously it's harder to leave open holes in the box if you don't want rain/snow/leaves/birds to get inside. They need grilles, louvers or covers etc.
