Are you just wearing a plain cotton shirt? If so, I suggest purchasing a fitness shirt that will wick the sweat away from your skin. Also, wear shorts (if you are not already).
I too am one of those people who sweat a lot, sometimes, it will happen without any intense physical work.
Apparently if your body sweats a lot you are built to be athletic. The body realizes it needs to be cooled and starts cooling itself right away.
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