First thing I test for with low body temps, particularly in the extremities, is iodine deficiency. See Optimox.com
for more information. The test is a simple 24-hour urine test.
I've had multiple patients whose cold hands and feet have gone away after completing the testing and then the loading phase of iodine supplementation.
No, a normal Western or even Paleo diet will not get one enough iodine, especially when coming from a deficiency.