Had same problem-overheat-shut down. I was using an external window box fan to cool it down. Another forum (I can't find it again!) said dust between the fan and the heat sink heat. Remove bottom cover 8 screws. Remove heat sink 5 screws. Remove and BAM a dust buuny between the fan exhast and heat sink. This AFTER I had blown it with compressed air. Clean put back together and it runs 2x cooler and 2x faster!! The post had a link to dell sevice manual for removing the heat sink
This fix worked like a charm.