Chips certainly are generally made of silicon nowadays, but they include a lot of components, such as solder and conductive metal that cannot take nearly as high a temperature as silicon can.
The fact that semiconductors can conduct better when hot has very little to do with it. If good conduction was all you wanted, you could make the chips of metal. But trust me, all-metal chips would not work.
The whole point is not to conduct electricity, so much as to control the conduction or non-conduction of electricity. In practice modern high-density, high-frequency chips run hot anyway. Touch the processor of your computer after it has been running for a while (which I strongly recommend you do not!) and you will burn your finger.
Let the chip get much hotter than its working temperature and it soon loses that conduction control and stops working. If you are lucky it might resume working when it cools down, but even if no solder has melted and you can see no visible damage on the chip, it may have been destroyed anyway; you may realise that the chips only work because specific atoms have been diffused into particular positions on the chip (sometimes billions of microscopic positions) and if you heat the chip too much, they diffuse out of position and no matter how functional that chip looks, it is dead.