over heating inverter

I have a 2000 watt continuous/4000 peak modified sine inverter connected using "0" gauge wire 1 foot from  a 12 v deep cycle AGM battery.  I put in a 400 amp in-line.  The inverter is rated 115 volts output.  I plugged a space heater into the inverter.  The space heater is 500 watt 12.5 amps.  After an hour of continuous use, the inverter alarm sounded and the inverter was hot to the touch, the inverter fan did not come on.  Could you please tell me what you think happened and why it happened? Is my inverter dangerous from over heating? I haven't hooked this up to my solar panel yet over concern that the inverter is bad.

Thank you very much.