most pieces of the airbox are made of Mg

Compare with V8, n.a., 4,8l :

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Are you sure? That would be strange since Mg (although lighter) is worse thermal conductor than Al. Are you sure it isn't (brushed?) Al?
Yet I really hope it isn't just a galvanized plastic.

Humm I think the airbox is still made from plastic. You can see 2 little vents on the engine cover, but that alone isn't really enough to let much cooler air pass through.

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can also be
maybe two-piece; only upper part in Mg - lower in Al
cause its no plastic, till the pipes and small things

Sorry I am a bit confused, which part of the engine are you referring to.

Btw, direct injection SI engines have better thermo efficiency and that means the combustion can occur at higher temperatures, which means the exhaust gas will be even hotter than usual. Notice the exhaust manifolds are thick looking cast alloy (not sure which type) items which seems to me can insulate the heat from the exhaust gas.

Perhaps air vents on a hood would help a lot at heat removal from the engine bay. I'm surprised the cars in the official photos doesn't have the vents (neither does the concept) - since the prototypes are featuring them.

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Still the ducts are made of aluminum - so, having very good thermal conductivity. No special insulation there.

I guess the airflow through engine bay (and especially between the engine cover & hood) is designed to cool the area sufficiently.

now i´m completly confused
on occasion I must throw a glance of it

Im confused too, but guys in BMW knows what they do

I wonder what is the temperature surrounding the turbos and the exhaust manifold. Is BMW going to have an official technical press release for this new engine?