The first application of bivvy sacks was for alpinists caught out overnight by a storm or darkness or both. They were designed as a minimal shelter to keep rain and snow away from clothing. Typically the user would not even be lying down, but would be sitting on a ledge, often tied in to prevent a fall. They were successful if you could see dawn the next morning, and recognize it as such.

The insulating value was nil. The makers of the current mylar varieties rave on about their reflective qualities which only applies to their ability to reflect radiant heat. That unfortunately is irrelevant, since the vast majority of heat flow in the typical outdoors setting is by conduction or convection (sitting on cold ground or in a breeze).

Bivys have "evolved," so that some now are basically very small (and expensive) tents. Still all they supply is a shield against the environment; the sleeping bag or clothing gives insulation