This is an interesting idea.
The collector consists of a glazed front, and an absorber that incorporates Phase Change Material (PCM) for heat storage. During the day, the PCM stores heat from the solar radiation. At night, the PCM gives up heat, and tends to maintain the outside of the wall that the collector is mounted on at a higher temperature. This reduces heat loss through the wall. The collector has no plumbing or ducting connections to it -- it just sits on the wall, and keeps the wall from getting cold at night. See the paper for more detail.
On the down side, you would have to cover a high percentage of the wall with these to significantly reduce heat loss, and they don't appear to be inexpensive. One wonders if you put the money you spent on the collectors into more wall insulation if you might not do better? Or, if you could not do better with a smaller area of normal collectors or direct gain windows?
It seems that the idea could be cost effective if the collector cost per unit area was very low. Perhaps one possibility for a low cost version of this collector would be to use something like the "Low Tech Garage/Barn Heater" wall glazing over a wall that has an outer layer with some thermal mass. This would behave in somewhat the same way, with the inside face of the high thermal mass outside layer maintaining a higher than ambient temperatures long after sunset -- it is a bit like a very large, but thin Trombe wall. The incremental cost for such a wall might be low. The Polycarbonate glazing is about $1 per sqft, and if the wall was already planned to be brick or some such high mass material, then the incremental cost of the "collector" would only be about $1 per sqft. It would also look nice.
This is a bit like Nick Pine's wall warmer, only covering the full wall instead of only a portion of it.
Something to think about?