Why is it always so cold when the temperature rises?

To cause fever, the center of thermoregulation, located in the hypothalamus, shifts the "norm" of body temperature upward. As a result, the usual body temperature of 36.6 is already perceived as low. This triggers the usual cascade of reactions, as if the body was overcooled. The blood vessels in the skin are narrowed so as not to give off heat; sweat glands are turned off so that they do not lose heat with evaporation; there is a tremor in the muscles to generate additional heat; subjectively, cold is felt, which motivates a person to further limit heat transfer and increase heat production (wrap yourself in a blanket, curl up, put on three pants, bask in a hot bath, drink hot tea). Gradually, the body temperature rises to the new required norm established by the hypothalamus - 37-39 degrees. When the goal is achieved, the feeling of chills stops. When the body needs to lower the temperature, the hypothalamus lowers the "normal" temperature and you already feel the heat. Sweat glands work hard to remove excess heat with evaporation. The vessels in the skin dilate to remove heat. You undress, increase the area of ​​sweat evaporation (lie no longer in a ball, but with outstretched arms and legs). Thus, the body is cooled. This explains why, after taking paracetamol, aspirin, you wake up with a sheet and blanket soaked with sweat.

Chills are a sensation of coldness associated with a spasm of blood vessels on the surface of the skin, the so-called "goose bumps".

With chills, muscle tremors are observed. A person says that he is “shaking”, “tooth on tooth does not fall.”
Most often, chills are a harbinger of fever caused by infectious diseases.
Sometimes chills occur without fever, for example, with hypothermia, severe fright or excitement. In fact, this is a defense reaction of the body in order to warm up and increase blood circulation.
Chills, accompanied by a rise in temperature, or fever occur due to the fact that the body has penetrated disease-causing agents - microbes or viruses, with which it must fight. To activate his defenses, he needs to raise the temperature, as a result of which, due to vasospasm, heat transfer to the external environment decreases, and internal heating occurs more efficiently.
However, the patient himself feels overwhelmed at the same time, feels cold, weak and aching.

Not always, but mainly because the ambient temperature is less than the body temperature, i.e. the body is hot and the air is cold towards you, so it seems that it is cold.

There is another version: The feeling of cold occurs only during a rise in temperature, and a critical rise, that is, rapid. It happens as follows. During the onset of systemic inflammation, a multitude of cytokines are released into the blood, which, acting on the thermoregulatory center in the thalamus, "shifts" the temperature bar towards a higher temperature (ie, the normal internal temperature is about 37, and after "correction" the norm becomes 40). The thalamus gives a signal that is perceived by the body as hypothermia (the difference is 3 degrees) and the body begins to intensively raise its temperature, and the only way to do this quickly is a tremor of all the muscles of the body, which is perceived as a chill. With a massive muscle contraction, a large amount of thermal energy is released, which raises the body temperature to a given by the thalamus.

Source: https://otvet.mail.ru/question/62548816