AMD fx 8120

Yes, the temps are a problem. Yes, they can cause some damage if you're consistently and constantly reaching those temps, but it's more of a long-term thing; otherwise, you would have been plagued already by thermal-instigated shutdowns and/or CPU throttlings (both being attempts by the system to deal with the temps).

Before you go for an aftermarket cooler, though, take a good look at your system. Whether you have an AMD chip or an Intel chip, there are only a few situations where you'll run into temperature issues with the stock cooler:

1. Bad environment. Basically, your PC tower is either located in a higher-temperature-than-normal location, or exposed to hotter-than-normal air from the environment. Make sure, for example, that you don't have your tower sitting on top of the HVAC outlet in your room (that works great when the AC is running, not so great when the furnace is running). Inadequate ventilation can also cause this -- for example, some computer desk designs have a "tower" compartment for your PC. It seems like a great space saver, until you realize that a) the 'barely wider/taller/deeper than the tower' compartment restricts airflow to your PC, & b) the backboard for the desk, even with those 'cable management holes' in it, mostly just redirects the hot air from the PSU fan/back case fan towards the front of the compartment, where it gets sucked right back in. Keep your PC away from hot spots, & make sure it gets plenty of air. That leads to...

2. Inadequate case airflow. This is especially a problem with mini-towers, "desktop" cases, & other cases that are small & designed for mATX motherboards. However, you can even run into problems with mid- or full-size towers, especially if you don't have enough case fans. It's not enough to have a fan to blow out the hot air from the case (in addition to the fan in your PSU), you usually want at least 1 other fan to pull cool air into the case. The more air that gets pulled in, the more it can cool off the components & the more efficient your exhaust fans work. Ideally, you should have fans installed in pairs (1 intake, 1 exhaust), with the intakes separated from the exhaust. Since you also have an exhaust fan in your PSU, as well as (usually) a fan system in your GPU, you may want to add an extra intake fan just to make sure you have enough cool air coming in. For example, in my case (see signature), I have 3 intake (bottom, right side, & front) & 2 exhaust (rear & top). The configuration lets my PSU get as much cool air as it needs, while all of the hot air from my CPU gets sucked right out of the case (which is freestanding, so that hot air doesn't come anywhere near my intakes). Case fans are fairly cheap, as even somewhat quiet ones will run you around $10-20 USD at most. If your case has room for them, try installing some extra case fans before trying to swap out coolers. They not only might help solve the problem, but they're a lot easier to install than a CPU cooler.

3. Space & cable management. Kind of goes along with #3. Essentially, anything that restricts air flow in your case is bad. Some cases have special sections that allow you to thread the power cables for your board & peripherals "under" or "behind" the board itself, so that they don't block the airflow. Also, a GPU generates a lot of heat, so if your GPU's fans actually exhaust inside the case itself, it might not hurt to see if you can maybe move it further away from the CPU so that it's not getting a direct shot of hot air constantly. Unfortunately, the options are usually pretty limited, as most boards usually specifiy where your GPU has to be installed for optimal performance, so you may not be able to make as many adjustments.

4. Thermal paste/dust on heat sink issues. Maybe it was a bad batch of paste. Maybe the old paste wasn't completely removed before a new layer was applied. Maybe too much was applied (almost seems counter-intuitive, but too much paste/too thick of a layer means it doesn't transfer the heat as well to the heatsink & cooler). Basically, if none of the other methods work, this is where you go. Completely remove the thermal paste with rubbing alcohol (& if you have to scrape it off, just be super, super careful), let it dry, then apply a very small amount (usual recommendation is "the size of a grain of rice"), & reattach the cooler. It would also be a good time to clean off that heat sink, as it's a literal dust magnet. Dust on the heat sink acts as insulation...which is bad, as that prevents the heat sink from emitting heat (its sole function & reason for existing). Compressed air works great, as you want to avoid anything that might generate static electricity (no Swiffer dusters!!!).

If that still doesn't solve it....

5. Bad CPU cooler. Congratulations (/sarcasm), you won the "Bad CPU Cooler" lottery! Or, you're using a CPU cooler that's simply become so old that it's not functioning properly. In this case, a simple air-based cooler is more than sufficient, especially if you're operating at stock speeds. Tom's has a laundry list of recommended models (http://www.tomshardware.com/reviews/best-cpu-coolers,4181.html), but even though it's not on the list the 212 EVO is still a good choice.