It would seem nothing but obvious to me that the human skin monitors the temperature of the outer skin, in order to make the body keep a steady temperature, but at the same time the interior (organs etc) function a whole other way. Inside the body is a much more constant temperature, and as such no sensory system needs to work on the inside of the body in the same manner as it does in the skin.
When the sensors in the skin "measures" a decrease in the skin temperature, it contracts the outer vessels, so less blood flows close to the skin surface, ie to lessen heat loss from the skin. If this doesn't help, we feel cold, and put on a sweater, turn up the heat etc.
It would make no sense if the skin sensors monitored the environment, as it is apt to change to whole time. The whole purpose of these sensors are to prevent deviations in the central temperature of the body, not in the skin, which is merely a "regulator".
If the temperature in the environment change to a large degree, it's another story. This spells "danger" for the body, and I believe different, and more serious mechanisms get into play in this situation. In such an environment, the skin temperature drops or raises so fast and so much, that the skin can no longer regulate, and thus compensate for the changes. I would imagine a further detraction of blood into the vital organs, and a "preparation" of an eventual loss of limbs by a more or less complete shut off of the blood supply to those limbs. It's the vital organs that keep us alive, not the limbs.
Therefore it's my guess that we have at least two different temperature sensory systems, and they work independantly of each other. I must repeat, that it makes no sense for the skin sensors to monitor the surrounding air/environment, but only the outer skin itself. Think of the chill factor; how quickly and abruptly it can change the skin temperature, and when we go into shelter it just stops as abruptly. We would use huge amounts of energy if we constantly monitored the air around us, which is why I believe this is not the case. Nature is smart!