You ask two different questions. Some people are allergic to peanuts and it is possible that in some a flushing of the skin might be involved so it is more apparent starting with cold skin. Are there other effects also and does the warming also include the face? As to circulation, what you describe can be due to many things, including age. But the cold hands are not likely caused by eating, or not, peanuts.
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In winter I usually have cold hands, even when I'm inside and the temperature is warm. I noticed that after eating peanuts (less than 100 g) my hands becomes warm. Could it indicate a circulation problem or is it normal?