Space heaters account for 33% of all residential fires and account for 75% of all residential deaths due to fires.
Landlords are supposed to provide adequate heating equipment for a rented property. In many states the local municipal laws will clearly state and call out by name that this means space heaters are not an acceptable means of heat. If you rent a property to someone it's not a stretch to specifically ban space heaters from being used in your property. The property has adequate heating devices installed, no space heaters allowed. By allowing space heaters in a property, you're potentially increasing your chances of a fire dramatically, by allowing them you're dramatically increasing your chances of a wrongful death lawsuit. I'd be drawing a hard line with these tenants, with an official company letter notifying them of their breaking the lease terms by operating space heaters in your property, I'd also be pursuing having them pay for the electrical problems you're paying for or at least notifying them that you're examining the issue and will be deciding whether they are liable for the damages.
Next time, next winter, or next month you could be instead answering the phone from the fire dept that your property burned down or the police that a tenant died or were injured in a house fire caused by space heaters that they have used because the landlord never said the couldn't, no record exists of you denying their use and then the next call is from someone's attorney suing you for a wrongful death, based on the precedent that at one time they had to use them because you admitted or inferred that there was a heating issue with the property due to them contacting you about an excessively high heating bill and at that time you were pursuing all sorts of corrections to the problem.
Instead I'd be telling the tenants there is nothing wrong with the place, stop opening the windows and space heaters aren't allowed.
I can't tell you the amount of tenants who have tried to tell me what was wrong with something based on a symptom. I had one in particular who would constantly call us to tell us what needed to be done instead of what the problem was. For instance she would tell me we needed to send someone out to snake the main drain line of the house because it was clogged. With interrogation it was determined that the drains weren't simply 'clogged' but that she had stopped up 1 bathtub drain by lack of cleaning her massive amounts of hair in the drain stopper. Cleaning the drain stopper of that single bathtub eliminated the need to have the main drain line snaked. She would tell us we needed to have the central air serviced because it wasn't cooling the house correctly, with interrogation we discovered she was leaving the AC off all day letting the house heat up to the high 80s when it was 100 outside, then coming home at night and she expected to be able to cool the house down to 65 degrees in 2 hours.
Just trying to say don't let tenants send you on wild goose chases, especially ones where you could be held liable by your actions from a cascading series of events.