The answer is complicated and probably inconclusive due to the number of variables. I am not an expert on this, so anyone please correct anything misstated here.
The bivy should trap an additional non-uniform sized layer of air (conductive/radiative heat loss reduction?), and cut down on felt wind (convective heat loss reduction?), while possibly retarding the loss of moisture (evaporative heat loss reduction) although not losing moisture is not good in a sleep system.
Besides keeping you dry, the convective gain (blocking the wind) is probably the greatest warmth advantage to a bivy. But bear in mind that is only works when there is wind ~ thus the complexity of the answer. As others noted, if the bivy forms a sheet of ice, there will be no further evaporation, but the trapped moisture will wet your insulation, possibly leading to a collapse.
My rule of thumb for the purposes of my calculations is that my eVent bivy adds around 5 degrees Fahrenheit. But it's real advantage is in what it prevents me from losing. That is, my 30 degree sleeping bag would probably not feel like 30 degrees if used unprotected in a high wind.