Another effect of the extra heat is that sea levels will go up. This is partly because polar ice is melting, and partly because seawater expands when it gets warmer. (Metal does the same thing, which is why you can loosen a ring that’s stuck on your finger by running it under hot water.)
Doubtful. Gold and other typical ring-materials expand about 15ppm per degree centigrade. On your finger they'll be like 25C as it is, and you couldn't warm them much more than say 50C before you'd burn your finger. An expansion of 25*15 = 375ppm won't noticeably help with taking of a ring. If the ring was 16mm diameter before, it'll now be 16.006mm
This doesn't really matter for the point of the book -- but it's symptomatic for Gates somewhat superficial knowledge about the topics and care in getting things *right* -- someone with a better foundation in physics would likely have a ball-park feeling than this can't be right and then go do the math. (like I just did!)