Here's a link to a very simple form of using thermal mass - in a primative ceramic heater to squeeze a remarkable amount of heat out of a single candle.
RV News Magazine | The Voice of the RV Industry
there are a couple of other threads that show homemade versions of this heater, and of course up until central heating became common, it was quite usual to put hot bricks or ceramic water bottles to heat your feet in a cold bedroom. Even canopy beds were originally made to create a mini-room within a bedroom, so that the occupants of the bed could be warmed by their own body heat not being allowed to dissipate into the room ... of course eating beans could make the enclosed area more than "just warm".
I even remember a tale or two from oldtimers who claimed they could heat an Airstream by turning on a couple of burners (on low) and inverting flower pots over them. Carbon Monoxide poisoning makes that sound just stupid... but perhaps if the fan vent were left open? (still stupid )
You might play with some terra cotta pots hung over the fire pit, both to diffuse the heat and to store it then give it up even after the fire is turned off. If that has a good effect, then you could start spending cash on ceramic logs.
Of course you could use some cast iron dutch ovens on the fire pit - cooking and warming the area too.