Here's a fairly simple model of fuse thermal behavior that I just made up, with made up values too. The model is surely inaccurate overall, but should accurately illustrate the issue here, just using I^{2}*R, and that heat transfer rates are proportional to the temperature difference.

- The fusible element blows when it reaches 150C (maybe it melts, maybe it just weakens and a spring overcomes its reduced strength)

- The fusible element is sized so that at the rated current it achieves a 90C temperature rise over its ambient temperature. The physical size of the fuse is independent of its rating, so the total heating from any size fuse carrying its rated current is the same.

- So in free air at 40C, the fusible element at rated current will reach only 130C and not blow.

- A normal enclosure and switch/busses are designed so that at rated current with the rated fuse size the internal temperature rise is 30C over the enclosure ambient. Let's say half of the heat generation comes from the fuse itself, half from the switch/busses.

- So at 40C ambient, with rated fuse and rated current, the normal enclosure interior would reach 70C, and the fuse would reach 160C, and blow prematurely.

- While if we reduce the current to 80% of rated, all the heat generation goes down via a factor of 80%^{2} = 64%, so all the temperature rises go down to 64% of the previous case. That means the 120C total temperature rise becomes only 77C temperature rise, and the fuse reaches only 117C, and it holds.

- A 100% rated enclosure and switch/busses are designed so that at rated current with the rated size fuse the internal temperature rise is 15C over the enclosure ambient. Let's say the switch/busses heat generation is the same as the normal enclosure, so the 100% rated enclosure is twice at good at rejecting heat, so you only get half the internal temperature rise.

- Then at 40C ambient, with rated fuse and rated current, the 100% rated enclosure would reach 55C on the interior, and the fuse would reach 145C, and hold.

With this model, what happens if we put a 1200A fuse in a 1600A normal enclosure and run 1200A through it? The heat generation from the fuse is unchanged from the case of a 1600A fuse carrying 1600A, as it is a fuse running at its rated current. The heat generation of the switch/busses is reduced by a factor of (12/16)^{2} = 9/16, but it was only half of the total heat generation.

So the new total heat generation rate compared to the old is 1/2 (the fuse) + (1/2) * (9/16) (the switch/busses) = 25/32 of the previous case. That means the interior temperature rise of the enclosure is only 25/32 of the previous case, or (25/32) * 30C = 23C. So the fuse reaches 40C external temperature + 23C enclosure temperature rise + 90C fuse temperature rise = 153C, and the fuse blows prematurely.

Cheers, Wayne