mark47n
Speaking as a licensed electrician it sound like you’re leaking ohms. You can get a fresh bag and pour them in the meter base.
In all seriousness, before you call an electrician go out to your meter and figure out haw quickly it;s turning. If it’s the old dial type see how fast it’s moving from number to number. Now turn on the heat (just for a bit) and repeat the above exercise, you shold see a marked increase. Record the time. One last step turn off everything that you can; lights, unplug all electronics, large appliance, etc and, again repeat. This is sort of similar to looking for a water leak in that you’re looking for a high impedance load where the current isn’t high enough to trip a breaker but still draws a fair bit of current. This is a serious hazard and rather uncommon in a residential setting. It’s also akin to a wter leak as you keep drawing Kw around the clock.
A good habit, also, is to find out when the utility’s billing cycle is and then record your meter readings at the same time (I can help you with that, if necessary) and see if your readings coincide with SCLs.