I just saw the phone temerature drop to 1*c whilst the battery temperature remains at 4*c. So whilst the battery temperature sensor was more quick to react to the environmental temerature (presumeably because it is on the periphery of the device unlike the internal phone sensor), the phone temperature sensor is giving a reading which is consistent with the area forecast for this area.
The elevated temperature of the battery could be explained in one of two ways:
1) The temperature sensor is out of range because 1*c is below the recommended operating temperature for the phone.
2) The power dissiapted across the battery is sufficient to maintain a steady-state temperature of 4*c.
I will bring the phone inside, turn off the GSM by putting it into flight mode in order to reduce the power consumption (and, hopefully, the power dissipation over the battery) and then sling it back out again . If this allows the steady state temperature of the battery to stabilise to a lower level then I am prepared to favour hypothesis 2 over hypothesis 1.