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I've tried web search but have not found that specific answer. As far as I know at least some people feel pain (e.g. in fingers) when exposed to cold for prolonged amounts of time. E.g. here sciencedirect - thermoreceptor

The temperatures that individuals report as painful vary, although temperatures above 45 °C and below 15 °C are generally considered to be painful.

As I understand 15 °C refers to ambient temperature, probably when full body is exposed to it for prolonged time resulting in gradually drop of internal temperature. But at what temperature at the thermoreceptors (nerve sensory endings) pain signals are produced and after what time threshold? Are they (temperature level and time duration thresholds) same for different parts of the body?

That answer here Why do people feel extreme cold at different temperatures compared to other people of same body structure? implies feeling depend on many things, like differences in clothing, distributions of body fat which does not look like they would change an answer to my question and some others, like neurotransmitter sensitivity which look to me like they could. However, I think there could be definitive answer to my question in the form of a reasonable range.

User Desiigner
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Final answer:

Pain signals due to cold temperatures are mediated by thermoreceptors and nociceptors, with the face and ears being particularly sensitive. Receptor sensitivity and the time threshold for pain can vary based on individual differences and other factors like acclimation. The body has mechanisms such as shivering and vasoconstriction to counteract cold.

Step-by-step explanation:

Thermoreceptors and nociceptors are sensory receptors that transduce temperature and pain stimuli, respectively. When it comes to temperature thresholds at which pain is perceived, it is important to understand that different parts of the body may have varying sensitivities. The face and ears have the highest concentration of thermoreceptors. Nociceptors respond to stimuli that might be harmful, including extreme temperatures. The experience of cold can lead to pain when exposed to temperatures below certain thresholds, which are usually considered painful below 15°C at the ambient level. It is important to note that local receptor activation and pain perception can depend on a number of factors including individual physiology, acclimation to temperature changes, and clothing, among others.

As for the time threshold for pain, it varies widely among individuals and is influenced by both the intensity of the cold and the individual's adaptability and sensitivity. Moreover, receptor density, as evidenced by a two-point discrimination test, suggests that different areas of the body may respond differently to temperature extremes, contributing to the variation in pain thresholds. The response to cold such as shivering or vasoconstriction is the body's way of trying to maintain homeostasis.

User Badal Shah
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