The box melted because of heat. Fuses themselves don't normally get hot - even high-current ones such as 50 amp.
If they are asked to carry unusually high current (because of a fault in the circuit somewhere) they blow. For a brief moment, the insides of the fuse get hot enough to melt. - but that's a tiny bit of metal, for a brief moment - not enough to affect the temperature of the holders and the plastic box. So it's not the circuit, or consumer, that's the problem.
Fuses DO get hot when the current meets a resistance at the fuse - in other words, when the fuse is not contacting properly with its holder. This might be because a fuse hasn't been pushed home fully, because the clamps are weak, or - most likely - because of some corrosion where the metals touch. As soon as a bit of corrosion begins, the point of contact starts to get warm ... and that encourages more corrosion.
If ever you find fuses getting warm, clean up their contacts.