Welcome to the forum, Steph!
You are certainly not the first one to report being colder after starting IF. Many have reported this. There are a few explanations I've seen for why this occurs:
1. Calorie restriction can reduce BMR (basal metabolic rate) and NEAT (non-exercise activity thermogenesis)
2. Calorie restriction can lower thyroid function, particularly T3.
These effects are not general and seem to occur only in some people. Regarding thyroid function, you might look into this. One way to get an indication is to check your armpit temperature upon waking in the morning before eating. If it is lower than 98F (36.7C) you may want to have your thyroid checked.
I have two recommendations that may help immediately:
1. Use virgin coconut oil. This can be used in cooking instead of oil or butter, but a very pleasant way to take it is to add it to your coffee or tea. The MCT oil in coconut is not only very healthful, but it increases thermogenesis and aids in weight loss, while providing a long lasting, even source of energy and warmth. I recommend 1 tablespoon per cup of hot beverage. You can take 1-3 tablespoons a day.
2. While fasting or calorie restriction can produce a "starvation response" and reduce your BMR, this is not inevitable. Robert Lustig describes and explains this in his great article on the hormonal causes of obesity:
http://www.nature.com/nrendo/journal/v2/n8/pdf/ncpendmet0220.pdfIn particular, he points out that plateaus in weight loss often result from a reduction in NEAT (or what he calls REE - resting energy expenditure) but that this can be reversed by driving basal insulin levels low enough. He proved this by giving obese children an insulin inhibitor (octuride) and finding that they both ate less and spontaneously increased activity levels!
So the key is to continue with your IF, but possibly drive insulin lower by adding in some intense spurts of exercise and add nutritional components that improve insulin sensitivity, such as fish oil, magnesium, chromium, and high dose vitamin D. I think that one of the advantages of IF over an calorie restricted diet in which you just eat low calorie foods throughout the day, is that IF really groves down basal insulin, but also periodically restokes the fires with a high calorie meal.
Good luck and please post your progress and results. Your experience could help others here.
Todd