There are many threads regarding malfunctioning Inverters. Just type in ' Inverter' in the Search box and you will see 5 or more pages of these. One of the things you need to check would be loose connections on your incoming wires from the batterries, thru the fused disconnect and onto the inverter. From your inverter to your 120 volt loads, was anything on at the time, it could be you overloaded the inverter and your 12 volt 200 amp fuse isn't seeing the overload. That may be why your solonoid is so hot.