Ok, your body temperature does not influence how hot or cool you sense something to be. Hot and cold are relative sensations. If you stick one hand in hot water, another in cold water, then both in room temperature water after a minute or so, it will feel hot to the hand that was in cold water, and cold to the hand that was in hot water. This shows that even if you account for your body temperature, you're still nowhere near accurate. Your hand is a few degrees cooler than your core body temperature anyway.
Simple answer is DON'T WORRY. The snake SHOULD feel cool to you. It is and that's right.