The following information was provided by Timerlane:

Orignally, the intent was to provide proof of something I had noticed before. It was popular opinion at the time, that Head/Arm/Leg cooling, existed, and raised the burn temperature of your AC, and reduced the rate at which the AC took damage from burn, but was not worth as much as core cooling; so earlier, I had attempted to find an equivalent set of cooling parts, that would make an equal burn temperature(I was hoping, perhaps, OVE/NER/RE/GG/ILC would equal MM/003/IKS/ALS/FLUID), using MG/1000(good source of slow, gradual heat)and/or HZL50(good, light source of fast, but not too fast heat), but to no avail.(If you look at the cooling ratings on the previously mentioned Heads, Arms and Legs, they are the the highest, and lowest of their respective classes, not counting weapon arms.)I can only guess I wanted to see how much cooling the Head/Arm/Leg combo was adding to the NER, so I swapped out the IKS for NER, and made the MM/003/NER/ALS/FLUID, took the MG/1000 to both of them, simultaneously, in Split Screen VS, only to find absolutely no difference in either the rate at which both ACs took on MG/1000 heat, or the Output Down or Danger Heat temperatures.

So, I finally got around to fully checking out, and confirming, this, and to finding how much AP is saved by the high Emergency Cooing SA77 Radiator, vs the basic SA44 radiator.(Sidenote: Maybe I'll do some comparisons with the CR14 and ICICLE, sometime in the future.)

Just like I mentioned before, I used these two setups:

Maximum Head/Arm/Leg Cooling Setup:
CHD-06-OVE/-/MAH-RE/GG/CLF-D1-ILC/MBT-OX/E9/AOX-X/WS-3/CGP-ROZ/RMR-SA44/CWG-HG-80/KWG-HZL50
OP-S-SCR, OP-E/SCR,

Minimum Non-Weapon Arm Head/Arm/Leg Cooling Setup:
MHD-MM/003/-/MAM-SS/ALS/MLB-SS/FLUID/MBT-OX/E9/AOX-X/WS-3/CGP-ROZ/RMR-SA44/CWG-HG-80/KWG-HZL50
OP-S-SCR, OP-E/SCR,

I compared them, using the same core with both of them, and found the following:

OB Cores
With MG/1000/HZL50:
AC____________OVE/IKS_____003/IKS_____OVE/STO_____003/STO_____OVE/NER_____003/NER
Danger Heat_____650_________650_________470_________470_________440_________440__
Output Down_____800_________800_________580_________580_________540_________540__

Pretty self-explanatory, it states the "Danger Heat" and "Output Down"(burn) temperatures, and shows no temperature changes between the High Head/Arm/Leg Cooling AC, and the Low Head/Arm/Leg Cooling AC.

SA44/HG-80 Burn Test
AC_________________OVE/IKS_____003/IKS_____OVE/STO_____003/STO_____OVE/NER_____003/NER
Start AP_____________9275________8942________8929________8596________8429________8096_
HG-80 rds_______________6___________6___________5___________5___________4___________4_
Post Burn AP_________8621________8277________8350________8007________7939________7599_
AP lost_______________654_________665_________579_________589_________490_________497_
HG-80 Damage AP_______258_________268_________233_________242_________201_________208_
Burn AP loss__________396_________397_________346_________347_________289_________289_

SA77/HG-80 Burn Test
AC_________________OVE/IKS_____003/IKS_____OVE/STO_____003/STO_____OVE/NER_____003/NER
Start AP_____________9275________8942________8929________8596________8429________8096_
HG-80 rds_______________6___________6___________5___________5___________4___________4_
Post Burn AP_________8782________8438________8492________8150________8060________7720_
AP lost_______________493_________504_________437_________446_________369_________376_
HG-80 Damage AP_______258_________268_________233_________242_________201_________208_
Burn AP loss__________235_________236_________204_________204_________168_________168_

Start AP: The AC's starting AP.
HG-80 rds: The number of HG-80 shots necessary to put the Core into "Output Down"(burn) Heat may have exceeded the rated "Output Down" temperature, so extra burn damage may have been taken.
Post Burn AP: The Amount of the AC's AP left after the said number of HG-80 rounds hit the AC, and burn has subsided.
AP lost: Start AP minus Post Burn AP.
HG-80 Damage AP: Beforehand, I fired 6 HG-80 shots at each AC, allowing it to cool between shots, and wrote down the AP for each shot, so I could find the amount of damage done by the Attack Power, of the ammo itself, without the heat.
Burn AP loss: AP lost stat, minus HG-80 Damage AP, or the AP lost purely from the burn.

Note that around 70% more AP is lost from burn with SA44, compared to SA77.

EO Cores:
With MG/1000/HZL50:
AC____________OVE/GRP_____003/GRP_____OVE/002_____003/002_____OVE/ORCA_____003/ORCA
Danger Heat_____570_________570_________500_________500_________420__________420___
Output Down_____700_________700_________620_________620_________510__________510___

Again, self-explanatory, it states the "Danger Heat" and "Output Down"(burn) temperatures, and shows no temperature changes between the High Head/Arm/Leg Cooling AC, and the Low Head/Arm/Leg Cooling AC.

SA44/HG-80 Burn Test
AC_________________OVE/GRP_____003/GRP_____OVE/002_____003/002_____OVE/ORCA_____003/ORCA
Start AP_____________9112________8779________8752________8419________8259_________7926__
HG-80 rds_______________5___________5___________5___________5___________4____________4__
Post Burn AP_________8543________8200________8155________7822________7761_________7428__
AP lost_______________569_________579_________597_________597_________498__________498__
HG-80 Damage AP_______223_________233_________251_________251_________208__________208__
Burn AP loss__________346_________346_________346_________346_________290__________290__


SA77/HG-80 Burn Test
AC_________________OVE/GRP_____003/GRP_____OVE/002_____003/002_____OVE/ORCA_____003/ORCA
Start AP_____________9112________8779________8752________8419________8259_________7926__
HG-80 rds_______________5___________5___________5___________5___________4____________4__
Post Burn AP_________8686________8343________8298________7965________7882_________7549__
AP lost_______________426_________436_________454_________454_________377__________377__
HG-80 Damage AP_______223_________233_________251_________251_________208__________208__
Burn AP loss__________203_________203_________203_________203_________169__________169__

Start AP: The AC's starting AP.
HG-80 rds: The number of HG-80 shots necessary to put the Core into "Output Down"(burn) Heat may have exceeded the rated "Output Down" temperature, so extra burn damage may have been taken.
Post Burn AP: The Amount of the AC's AP left after the said number of HG-80 rounds hit the AC, and burn has subsided.
AP lost: Start AP minus Post Burn AP.
HG-80 Damage AP: Beforehand, I fired 6 HG-80 shots at each AC, allowing it to cool between shots, and wrote down the AP for each shot, so I could find the amount of damage done by the Attack Power, of the ammo itself, without the heat.
Burn AP loss: AP lost stat, minus HG-80 Damage AP, or the AP lost purely from the burn.

Note that around 70% more AP is lost from burn with SA44, compared to SA77.

It's interesting to note that both GRP and MX/002 lose the same amount of burn damage AP, from 5 HG-80 rounds(and about as much as STO), though the GRP has a higher burn temperature. ORCA burn damage is virtually the same as NER, despite it's extremely low rated in-game stat; though burn temp is a bit lower.

So, in conclusion: the Cooling rating on heads, arms, and legs, appears to be completely useless. The core and radiator determine everything significant about cooling, and having a high Emergency Cooling radiator will save you some AP whenever your AC enters Output Down. While the 150-ish AP saved here may not seem impressive, Emergency Cooling knocks your heat down faster once in burn, meaning opponents may not be able to "milk" as much extra damage out of the "burn", by hitting your AC with heating weapons, such as the RF/220, HG-80, HG/100, etc, that can keep your temperature up, and keep you in "burn".