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Obviously the heatsinks won't burn you. Let me give you an example: on the Intel boards, the southbridge chip hasn't got a heatsink. It's near the CPU, the VRM and stuff (heat sources). It gets real hot without a fan. You can touch it without hurting yourself but I wouldn't want to press my finger against it for more than an instant when the board is under load. 65C is enough to give you serious burns after only a few seconds. It's not just warm! I don't want to encourage you to damage your board by sticking your fingers everywhere but if you're careful you can in principle touch the chips without damaging the board (at your own risk! this isn't professional advice). If there's nothing hot enough to burn, the readings may be off.
Unless Gigabyte put something on that board that heats it up, it shouldn't run as hot or hotter than a fanless board... and yet according to your readings it does. In any case I wouldn't worry too much. If Gigabyte chose not to put better heatsinks on them, the components must be able to handle the temperature. Low-power boards shouldn't fry themselves in such an open case at 20C ambient... especially not if they've got a fan to move air around a bit. Boards which fry themselves in such a situation should come with a clear warning from the manufacturer.
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