Gas fireplace draft +blocking vent?

We have a Heat-n-glo gas fireplace in our home. We never use it, but last month our gas bill was over $400! Poking around I found out that there's ALOT of really cold draft coming from the gas fireplace. There's draft coming in from the little lip at the top, a couple small holes on the side of the fireplace, from the bottom section where the pilot light and all other mechanical parts area...basically from everywhere.
Is there anything that can be done to block all of the cold air from coming in? The room is freezing cold and I can continue paying $400/month gas bills. We keep our house on 68 which is cold to us but still doesn't make a difference.
There's a vent opening on the outside of the house (think it's called a trapezoid termination cap) where it's obvious that's where all the cold air is coming in through. Are we allowed to just cover that up with something so no cold air comes in? Or possibly unscrewing the cap and covering the vent pipe that's sticking outside of the house with some sort of cover (even like a piece of cardboard) to at least block all that cold air from coming into the house?
Any help is much appreciated! Thank you!

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