Silicon's band gap (1.11 eV) corresponds to 1110 nm (NIR), and any photons with more than 3 eV energy (413 nm) are lost (and all the excess energy in photons in between is lost as heat). Newer cells are around 0.6-0.7 eV, but I don't know their maximum capture energy. That's all the violet light and UV. There's a startup that makes a polymer film that can create two lower energy photons in the band gap from a high-energy photon to capture some of that wasted light. This would seem to be a cell that could capture it directly. Very very cool; that's a lot more energy captured per photon.
What I'm unclear on is why you need to heat it up so much to get to those efficiency levels, and it wouldn't just work as an ordinary solar cell.