Drain all the coolant from the engine block plug (enough DIY's on here) - check for oil in the coolant.
Drain all the oil - check for coolant in the oil
In both cases the visible signs will be a milky brown streak through the liquid
If you find it in either I would suspect the head gasket blew when the aluminum head got too hot.
If you suspect the head - go to a local shop and have them to a pressure test.
Changing the head gasket may not fix this - if the head warped from the overheating.
There are lots of threads on here about overheating including mine (325 cab)
I was lucky and the head did not warp - others have not been so lucky.
I will attach a PDF that is a BMW SI for checking the overheating damage of the E46.
Typically if this pipe is melted BMW determine that there was sufficient heat from the ovberheating to cause substantial engine damage.