Could the Lenovo Idea-Pad s405 record minecraft with fraps and not overheat?

It certainly looks good enough to run Minecraft, but instead of Fraps you could try recording software that uses less system resources, therefore putting less strain on your system. One such program is Bandicam. It should result in less of a performance hit than Fraps. Regardless of which you use, trying it out won't cause any harm!