It depends on the alternator that is installed and how the engine is set up to run. My Toyota Matrix 2005 will adjust idle speed of the cars engine to put out a proper charge voltage for the battery and provide 500 watts at a slightly sped up idle speed. The best thing to do is run a test cycle with conventional light bulbs to load test the inverter/auto at idle while monitoring the voltage as you slowly increase the light-bulb/load and see what level produces above 12.7 volts or so at engine idle....most current day autos should do the job though much depends on the inverter and alternator installed plus any extra loading caused by the power needed by the wood stove to run the heater to start it/run blower,etc etc.
500 watts will need 50 AMPS from the auto battery/alternator or maybe a bit more as many inverters are not so efficient when run as sine wave/ Other things to remember is that the auto is intended to maintain cooling while the auto is in motion and when just at idle you can over-heat the auto and cause much more heat and wear on fan belts.cooling hoses etc .Most autos turn on auxiliary electric fans when air conditioning is engaged or when the heater is on you can also get some added cooling from that being used.
Use the search bar and you can find some things I already wrote on the subject of auto....inverter....power for home emergency.
