Fire burning is a combustion reaction, which is a type of reaction that is always EXOthermic (meaning it gives off heat). When the carbon in the wood reacts with the oxygen in the air, it forms CO2 and H2O, releasing heat in the process that escapes the fire place and transfers out to the room.
As for the spread of heat:
“A fire can spread by radiation when the heat travels through electromagnetic waves in the air” -FireSealsDirect
