Possibility of combining photovoltaics and solar thermal energy In a private setting, photovoltaics and solar thermal energy are often harvested on the home's roof and roof area is limited. So, I thought about combining both, i.e. mounting solar collectors underneath solar cells. The rationale behind this is that the solar cells appear almost black and probably heat up considerably under irradiation. So if the collectors are in tight thermal contact to the cells, the water in the collectors might carry away the heat as usable energy, and possibly even increase the lifetime or efficiency of the cells due to the cooling effect (but this is rather engineering and not part of the question). So roof area is exploited twice (in two different wavelength windows). Moreover, if electric energy from the cells exceeds actual consumption and the battery's storage capacity, it might also be used for heating (albeit at a lower total efficiency, of course).
Can the amount of (infrared) radiation that gets absorbed (or possibly transmitted) by solar cells, and which is available as heat at the back side of the cells, be quantified by a rough calculation and either prove or disprove the benefit of such a concept? Does the almost black appearance of the solar cells fool one into thinking that they also absorb in the infrared, although they don't?
 A: From this site comparing solar panels,

solar panels are usually able to process 15% to 22% of solar energy into usable energy, depending on factors like placement, orientation, weather conditions, and similar.

As all the energy has to be absorbed, the photovoltaic  if in contact would be loosing only ~20 percent of the direct light so it will depend if it can be placed in contact.
It seems your idea though is already commercial.
A: Temperature of PV panels increases significantly during the day and their conversion efficiency decreases with increasing temperature. I had access to measurements of a PV plant and it showed that the total power production was about the same in August (middle of summer) and October (early fall). Although the days were shorter and there was less solar irradiance in October vs August, the air temperature was significantly lower making PV panels more efficient. For the outside temperature of 35 C, the PV panels can easily reach 70 C!
Here is a map that shows power output of a PV panel versus incident solar irradiance and PV panel temperature. This map was generated from the equivalent (single-diode) model of the PV panel. It is probably a bit difficult to read the map, but just follow the yellow line. Power output at (600 W/m2, 30 C) is about the same as for (700 W/m2, 80 C). These numbers are realistic for a typical summer day - air temperature up to 35 C and PV panel temperature up to 80 C. It takes 15-20% more solar irradiance for the same power output when panels get hot!

Figure 1. PV panel maximum power output vs solar irradiance and panel temperature (Source: M. Gulin, PhD Thesis, 2019)
If you cool down PV panels directly, you might increase their power output and get some usable heat. In order to do so, you would have to mount some heat exchanger on the back of PV panels and there would need to be some fluid flowing which would take the heat. If you take into account that you need to pump this fluid, which also consumes some electricity, with all these benefits the overall efficiency would not probably increase by much, if at all! I was mentoring a student a while ago that did their thesis on this topic, and rough calculations showed this concept is not viable. However, they were not considering heat pumps in their calculations, just a cold water flowing and taking the heat. The commercial product @annav mentioned in their post probably uses some sort of heat pump to increase efficiency of taking the heat from PV panels.
