What kind of heat do you have-electric?...heat pump?----this dramatic change deserves a service call from your dealer...

IMO

Do you have electric baseboard heating?

You probably have electric strip heat in an air handler or some people call it an electric furnace.

Your AC is likely just straight AC with no heat pump option. Heat pumps cost more and so people in warmer climates tend to go with the cheaper non heat pump option... or straight AC with electric heat.

The reason your bills are high:

1 electric strip pulls 20 amps. (5kw)

2 electric strips pulls 40 amps (10kw)

depending on the size of your house and your HVAC system you could be pulling up to 80 amps. That is one heck of a load.

Here is another factor: what rate do you pay for electricity? like cents per kilowatt.

So how does a heat pump reduce your utility costs?

A heat pump has controls that reverse the refrigerant to send the heat indoors during the winter months. Because of that (if you have a heat pump) your heating bills are typically similar to what you pay for AC.

In one (cold) winter in a warmer climate a heat pump will easily pay for itself (*if you have electric strip heat as heating system). Problem is many areas in the south only experience the cold we have this winter once in about 20 years. Last two winters here (Katy, Texas area where I am) there was no winter, other than a few brief chilly snaps.

Honestly, I would run a portable infrared heater or two over that system... way too expensive. I would suspect a short of some kind causing extra large energy losses, but not enough to trip the breaker. Should have it looked at, and something else used until it can be serviced. Everyone should have a backup plan if their furnace goes down anyways. There are nicer looking ones if concerned about looks. They can handle up to 1000sqft by themselves.

Where do you live? I assume it’s not really a cold zone if you are heating only to take the chill off below 50. So given that, 500 dollars a month is a really high. Particularly as your summer AC costs are relatively low if you are cooling the place to 70 degrees. Living in the cold North in New England , I only spend 2000 per year heating with oil (plus probably 20 per month in electric to run pumps etc. ) if you are spending that muc, it might be worth having an HVAC professional calculate your actual heat loss (often referred to a Manual J calculation) , evaluate your system and recommend a better matched more energy efficient system. I suspect the payback period would be relatively short given how much you are spending monthly for heat.

Someone on this forum had a similar problem. In that case the issue was the electric heat strips were always on.

and sometimes it is an element in water heater that needs replacing. too many variables to give specific advice.

It's a shame when people spend their own time trying to respond helpfully to a question and the original poster goes AWOL.