Some of the older models work while charging. For example the MG7790 or MG7750/49 (not to be confused with the new version 7910/49).
The reason I know this is because I recently bought one from amazon specifically because I want it to work while plugged in but they sent me one that doesn't (MG7770). I sent it back and now waiting for the correct one to be delivered.
If I remember correctly, 60c is the temp that kills dust mites.