New cooler. (or if the paste/pad has been there for several years maybe just remove that and install some paste)
Replacing a case fan will have minimal impact on the CPU temperature.
*Considering the hassle to replace a stock cooler, I'd just buy a cheap one and setup an optimal fan profile. This will also make the computer QUIETER than it is now.
a) Cooler Master Hyper 212 EVO
b) Cryorig H7?
I say "?" because you want a 3-pin fan on the cooler if that's what your CPU_FAN supports on that older motherboard. Probably your motherboard is 4-pin, and in that case it MAY or MAY NOT support 3-pin so if it's 4-pin on the motherboard get a 4-pin fan (PWM) CPU cooler.
DO. NOT. GET. A. 4-pin. (PWM). FAN. IF. NOT. 4-pin. CPU_FAN. ON...