Ah! What cooler are you using? How many pins does it's fan connector have? If it has four pins (the stock cooler has this), set fan control to PWM; otherwise, it must be voltage-controlled.
Setting a 3-pin fan to PWM would prevent it from spinning properly, which could explain the beeping and would explain the higher-than-expected CPU temps at/near idle.
Your temps at/near idle should only be a few degrees above ambient, depending on your case cooling and CPU cooler; 60+ tells me your fan isn't spinning since your voltage isn't going nuts.
72.4c is max Tcase (the package), 100c is TJmax but you shouldn't go above 90 fully stressed.
The cooler is the one from intel that comes with the cpu (4 pins), the fan does spin, the max RPM I've seen in the BIOS is 2800RPM. As soon as I turn on the pc and I get into the bios the CPU temp shows 48c.
Now on the bios I changed VCore and PLL from auto to normal, also I went into win7 power settings and changed "maximum processor state" from 100% to 99%, also disabled intel turbo boost 2.0 on the bios.
Now the temp never reaches 60, it stays between 48c and 53c, cpuid show max 58c on one core, the others all 55c.
On my older pc temp is not a few degrees above room temp either, its about 50c all the time, 58c with load.
Maybe I should change the thermal compound, I did it a few times in 4-5 years on my older pc and that decreased the temp a little.
With SpeedFan software it looks like I only control the gpu fans, I have 4 fiels to move from 0 to 100%, only one seems to work and it controls the gpu fans, i tried settings the others to 0 then to 100, and no other coolers seems to have any effect.
btw this is the first pc I dont build myself, and it seems to be the one that needs more customizations je
update: I downloaded easytune6 from gigabyte, and disabled smart fan, now the cpu fan looks like it runs faster, because it does some noise (i think it comes from there because gpu and other case coolers hasn't increased speed) and it feels like it blows more air if I put my hand on the side of the cpu, core temps are between 47c and 51c now. Is there a way to run all fans at top speed all the time without a soft? I dont care about saving power or getting a quiet pc, im with the speakers turned on all day i dont hear anything anyway