Extremity
The extremities in medical language are not freezing cold or scorching heat but rather the uttermost parts of the body.
The extremities are simply the hands and feet.
The use of 'extremity' to mean a hand or foot is quite ancient.
According to the Oxford English Dictionary, it dates back to 1460-70: 'He schal waische al his body and his extremytees...(he shall wash all his body and his extremities...).'