I should've read JDFan's comment better. The i7 CPUs come with the cover, yes. The HSF's don't as far as I know.
37C is a decent idle temp.
That might be the case with the AMD CPU also -- I just remember there being a thin plastic cover attached to one or the other that I almost missed
- not sure if it was the HS in addition to the heavy plastic cover or on the CPU !