E34 Air Filter Pipes

What do the pipes, that are part of the cooling system, do that go to the air filter box?
I managed to snap one, the one that has the part where the pipe
connects on the top? I've managed to put the pipe over the hole and fix it on useing the clip, and it seems fine, it doesn't over heat, there isn't any leaks and the temp gauge stays at normal operrating temp.
But, I'd obvioulsy like to know what these pipes are for, and why they go in to the air filter box?
Thanks
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Tell me, why would coolant pipes go to the air filter housing?

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If I have understood the query, I think they might pre-warm the air..
I had one BMW where filtered cold air pipes went to the ECU box, presumably to cool the electronics..
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