This is exactly the definition of every small beekeepers honey, and some larger beekeeping operations too. A least in Sweden, and also UK I guess where most honey produced are done so by small beekeepers. So if "raw" is the definition of nearly all not imported honey, why use it?
And a complication are, it's not really about temperature, it's about temperature and time. I would much prefer heating honey to 50 degrees C during five minutes, than heating to 40 during five hours.
Vast majority of beekeepers fine filter. It's taught so the honey looks better and they can compete in shows. Most of them overheat, many don't use effective controls. Hive temperature is 35 Degrees, everything above degrades. That's BBKA and SBA, also international norm. 40 Degrees is widely accepted for practicality and destroys only a minimum of enzymes. Overheated honey is still sweet but has no or only few nutrients and medicinal properties. We call it Baker's Honey. Nothing to do with the extremely valuable bee product. Can't be sold as Honey.