I'd say it is fairly imposible to repair by yourself. You'd need to know what is the faulty part, and actually get the replacement from somewhere, and the tools to repair BGA chips are not that easily to be found.
You propably could, but where would you get the replacement motherboard? I'm fairly sure you cannot find it anywhere for sale.
That's the only real option. How come it's so expensive? I would have thought it'd be 50 bucks max.
You could experiment with alternate OS'es, use it as a development device for new HW, whatever
Are you sure it is heating up because it is trying to access the SIM? I'd rather think there is something broken so that it causes a large leakage current thru a chip, and that is causing the heating. If you knew the broken chip, and if you were in luck so you could identify the Vcc pins (and they were accessible, not under BGA...) then you could just cut off those pins and be done with it