pills can occasionally have a very minor impact on body temperature, as the progesterone in the pill does raise body temperature a small fraction. However, it is very unlikely that you would actually be able to perceive this change in body temperature.
It is much more likely that you are experience a flushing or clamping down reaction of the small blood vessels in the skin, causing your skin to feel cold or warm. This is a well known side effect of birth control pills. Sometimes it is necessary to switch to another form of birth control, especially if you are experiencing episodes where your fingers or toes go cold and white or blue (known as Raynaud's phenomenon).
Finally, it is possible that the sensations you have are related to another medical problem entirely. For example, hypothyroidism, caused when the thyroid gland does not produce enough thyroid hormone, is one of the most common causes of feeling cold. Other symptoms might include weight gain, changes in mood, changes in the hair, skin, and nails, or menstrual irregularities. This condition can be easily rule out by your primary care doctor
with a physical examination and a few simple blood tests.