Whenever there is a problem between you and the CFE (you say you consume a certain amount, they allege differently) they will offer to 'check out' your home or business to determine what your consumption 'should' be. They call this a 'censo de los aparatos' where they will go from room to room counting lightbulbs, television sets, fans, air conditioning units; anything and everything electric. They will then determine, based on average usage tables that they have made up, what your consumption really should be. They will then propose that as what you should be paying.
The word they is bold for a reason. They decide how you are using your aparatos electricos. If you tell them 'but I only use my blender once a month for the MEL margarita nite' they will just nod and smile; 'Sure you do.' There is not much of a recourse for you once you have gone that route. It will be up to you to somehow prove that you are really not using that air conditioning unit: it's your word against theirs and they are holding all the cards. If you lodge a complaint with the CFE you lodge it with them. What possible motivation could they have to fix your problem? There is of course, the PROFECO, but be warned that a fight with the CFE will be costly, time consuming and they will probably cut off your service for the duration.
As a foreigner, it's easy to be taken in by the politeness of the fellow asking you for permission to come into your home. My advice, from the cynical Mexican Yucatecan POV, and from years of experience living here and talking to other Mexican Yucatecans is to politely but firmly deny them this access. Once you do, it's like the Miranda statement thing police in the U.S. tell their arrest victims "anything you say or do can be held against you..." And it will be.