The AMD A8-5600 is an APU yes? That means it includes an AMD Radeon HD 7560D?
https://www.newegg.com/Product/Product.aspx?Item=N82E16819113281
Temp Monitor
I do not use HWmonitor and I uninstalled AI Suite 3 cause it gives me problems on Windows 10.
I use Hwinfo64. But since it is an AMD APU I recommend AMD Overdrive
http://www.amd.com/en-us/innovations/software-technologies/technologies-gaming/over-drive
I've looked around on several forums and the general consensus is that the AMD Trinity's temp sensors are (supposedly) hopelessly borked and dont monitor temps very well with software. Several people have said BIOS and software that came with a motherboard actually did read out the proper temperatures.
Some have had luck with Hwinfo64 view this https://www.techpowerup.com/forums/threads/amd-a8-5600k-temperature-reading.194811/
Temp impressions
80C by only running an antivirus? o-o That's insane!
you said "AI Suite 3 shows from 38°C to 52°C" and your house is around "30C" so I think that is likely the accurate one.
AMD's Sugegsted Maximum operating temperature is 75°C
So what is the Maximum operating temperature (Tmax)? It's the highest temp at which a CPU or GPU can operate at full capacity. But fear not, if you're CPU or GPU reaches this temperature it will not burst into flames.
Modern processors and video cards have overheating safety measures that prevents them to damage. Usually when the maximum operating temperature is reached the CPU or GPU will underclock itself to reduce it's core temperature. This will result in massive FPS drops in video games, for a few seconds.
Reaching the maximum temperature for extended periods of times will eventual damage your processor or graphic card, so focus on finding the overheating source problem.
cooler suggestion
I use this one for my 6700K overclocked doesn't go past 71 and its a push pull cooler not too expensive either.
http://www.coolermaster.com/cooling/cpu-air-cooler/hyper-d92/
I would not recommend standalone water coolers for example CORSAIR Hydro Series H60
These all perform worse than a good Air cooler.
try to research some air coolers for an FM2 socket CPU. Just make sure they fit in your case.