As a guess:
If this is a SD/HD settop box (STB) (no recording capability) it may have a cooling fan and the bearings in the fan are starting to fail. You would have to get another box from Verizon....
If this is a STB that is also a DVR it has a hard disk used to store your shows. It may also have a fan... In either case the bearings in the fan or disk are starting to fail.... Once again, no choice but to have Verizon replace box....
Is there a Verizon FiOS Store (not a cell phone store) near you where you could walk in??? Before walking in call tech support and get a case started so that service center will have paperwork when you come in.
Post mfgr and model number of yout STB.