BF4 and the newer version BF:Hardline are extremely CPU-bound games...assuming you are playing them online, and are on 64 player maps. On 64 player maps, it takes a very strong CPU to keep framerates up. That said, you'd probably be okay, if you'd spend $20-30 on a cheap but decent tower heatsink, such as the ones I linked below, and run your CPU @3.5Ghz, if not higher. Just remember, the larger the cooler, the better the cooling, and also the quieter it will be, when not running your CPU at 100%.
http://www.newegg.com/Product/Produ...$$$$$$$;35-103-099:$$$$$$$;35-103-064:$$$$$$$
And you've talked about so many video cards in this thread, when you say "the card", I have zero idea of which card you mean. If you want to take my advice on video cards, it wouldn't be wise of you to buy any video card for that system, except the AMD 290 or the GTX 960. Yes, the 960. It's 15+% faster than the GTX 950, and only costs ~$20 more. It also does 100% of the cool stuff that the 950 does, like hardware decoding of 4k video, recording games, etc, etc. The 290 is considerably faster than the 960, but you'll never know it, with your current CPU, unless you overclock it as far as it will go. Even overclocked, your CPU will never be fast enough to keep up with a 290.
However, if/when you decide to build yourself a new computer, the 290 I linked earlier will give you
considerably better framerates than the 960...with a CPU that's twice as fast as the one you have now. I only mention that because it's nice to be able to transfer old parts to new computers, and not feel like you're holding the new computer back a ton, the way you would be with a slower card. That would allow you to be able to let your wallet recover for a month or two (or six), before buying a newer, cheaper, yet still faster newer generation video card.
My last bit of advice for you, if you are wanting to build yourself a new computer/have one built for you, this is a very excellent time to do so. The Skylake architecture is as impressive as Haswell was over Ivy Bridge. It overclocks well, the chipset you want to buy with an unlocked Skylake is extremely nice, and has no major flaws, which Intel happens to be known for having in their first generation chipsets. What we always say around here is "the proper time to upgrade is when your equipment needs upgrading."
Just remember this, though: for the last 3-4 years, your problem has been your slow video card, not your slow CPU. Video cards, and that goes double or triple for cheaper ones, should be replaced often. For the past ~5 years, there hasn't been a whole lot of advances in CPUs, so not much of a reason to upgrade them. A gaming machine needs its video card replaced much, much more often, to keep it current and to be able to play the newest games. Good luck.
edit: One last thing. If you think you'll probably not replace that computer in the next 12 months or so, you'd be better off with the GTX 960. It is a much better match for your slower CPU, especially since AMD cards require more CPU horsepower to push them, and although it's only ~2/3 as fast as a 290, it's still 500-600% faster than your current card.