The "White Trash" budget build

The 880GM-LE is a low end 3+1 phase board with low end design, and I would not trust it for running 125W TDP processor.  Although it is rated for such, you will probably very quickly experience protective shutdowns that may affect your saved work as the motherboard's VRMs may not in all situations be able to push the processor.

In particular since you have an aftermarket H60, you make things infinitely worse by leaving a low end VRM system without ANY cooling whatsoever (neither airflow no heatsinks), preventing any effective radiation of heat - AND overclocking and overvolting to 4.2Ghz.  You NEED to pursue a new motherboard for proper operation with such power loads - and for now, you should use the AMD stock cooler to provide motherboard component cooling and undervolt and underclock as/if necessary, NOT overvolt and overclock.

You should take my warning and read the link in my sig (About VRMs & MOSFETs).

You are at least lucky that this board has a confirmed method of VRM protection because that shuts things down upon overheat/overload (you might not notice this right away but placing extreme load on weak VRMs degrades its ability to handle current similar to how a PSU degrades with time, eventually reducing the amperage supply/conversion capacity to the point where it will simply not work anymore), if it didn't you would be dealing with a flaming, burning mess instead of a motherboard.  It is extremely important that you know about the motherboard you are dealing with (i.e. VRMs capable?) before you proceed with an overclock/overvolt (i.e. is iteeven safe to do so).  Many recorded VRM failure incidents are caused by users' lack of knowledge about this issue.  That's what I and my article are here for.

By the way, 980 BE is a Deneb.  There are no cores to unlock.

The warm air exiting from the stock cooler is better than no air at all.  The likelihood is such exiting air is still cooler than the temperature of the motherboard component and thus there is still a capability of removing heat.  The case's two exhaust fans should be able to remove this heat that is pushed back into the case fairly quickly and efficiently.

Stock coolers normally blow downward and motherboard components are organized to be laid out around the CPU for this exact purpose.

You can probably expect that the lower side fan exerts low static pressure which means that the GPU fan and the H60's fan should steal most of the air that would supposedly move towards any motherboard components.  There is NO airflow going through them as it is likely skipping the setup.  You can't really relate the case ambient temperature to component temperature because hardly any of that component temperature is even radiating to the case; it's just sitting there and piling up without radiating naturally due to the lack of airflow.  That is what is extremely dangerous.  As much as 70% of all recorded VRM failures pointed out in my article (that was a measurement taken longer ago so it may have changed slightly as new failures were recorded) happened on setups where proper VRM cooling was not ensured (i.e. tower cooling/water cooling).

You should not ignore my warning by keeping your setup as-is until a new motherboard is claimed and I strongly recommend that you replace the AMD stock cooler for the safety and operating efficiency of your setup.  You are pushing a load that is well beyond what a board like this should be expected to handle.

Are those idle or load temps?  It's better to have higher idle temps and lower temps that remain more constant when loaded, rather than having low idle temps and ridiculously high load temps that raise continuously due to the lack of cooling and thus the over-time heat pileup.

Regardless of whether you've got the H60 or not you should put focus on case airflow.  Your H60 has extra 120MM fans; use them.  Mount them in the case to provide extra intake and exhaust so that the ambient air in your case actually gets out and cool air gets to your parts.  Cable management is also an important level of organization.  You took a first step forward towards better mobo component cooling by replacing the stock cooler, now you just need to take the other step forward that is improving case airflow.

If the components that are being measured by the mobo temp sensors (which do not measure heatsink temps but temps of the components under them) are cooler than the heatsink that you point out with the sensor, that probably means the heatsink is working - and is able to offload the heat from the component to the additional metal.  All you need is for air to hit that surface area and you're truly moving the heat away.