Uhh, not unless you live in an oven. I would just hold off on the cooler. If you don't plan to overclock, there's no use for it and if you end up wanting it it's easy to order when you actually do.
As for your build, do you really need an 8-core cpu? It's good for futureproofing but if you don't do much for productivity (as in, videos, encoding, and other multithreaded applications) you really won't notice much of a difference
Hm, if this is the case I could take and drop my cooler off my rig, I don't really live in a oven but it can get up to 90 degrees in here during the summer.
The CPU I'm getting is also a quad core as well so that'll generate some heat.
During the winter and when I have my own room I keep it like 50 degrees so I know that won't be an issue. But I don't have a room, now of course theres a chance that this room won't be able to get too warm itself.