I don't think there will be any special difference between 6700K and 5820K regarding heat if you will use air cooling ( with good airflow in the case ). At least I was comparing both and I haven't seen big difference on air. AIO can generate more noise in small case and then you will see that 5820K heats up a bit more.
If he decides on 5820K then I recommend micro ATX mobo/case as it won't be much bigger than ITX ( I mean whole PC ) while it's easier to make good airflow ( mainly near graphics card ). It will also use quad channel memory.
Looking at all games for past 5-6 years I can say that any new CPU will be good for next 3-5 years. Most new games are or based on old engines or designed to work on PC and consoles at the same time ( AMD APU which is already slow ) or require fast GPU more than CPU. Probably new graphics will be required faster than CPU.